Very complex, you should ask each individual question, or give more points general strategy: get 1 side to equal 0 factor set each factor to 0 solve
1. factor out the x and set each to zero x(x+7)=0 x=0
x+7=0 subtract 7 x=-7 x=0 or -7
2. factor out the 6s 6s(s+3)=0 6s=0 s=0
s+3=0 subtract 3 s=-3 s=-3 or 0
3. I'm assuming that the equation was supposed to be t^2+8t+16 so find what 2 numbers multiply to get 16 and add to get 8 the numbers are 4 and 4 factor (x+4)(x+4)=0 x+4=0 subtract 4 x=-4
4. find what 2 numbers multipy to get 25 and add to get -10 the numbers are -5 and -5 factor (x-5)(x-5)=0 set each to zero x-5=0 add 5 x=5
5. subtract 16 from both sides h^2+6h-16=0 find what 2 numbers multiply to get -16 and add to get 6 the numbers are -6 and 10 factor (h-6)(h+10)=0 set each to zero h-6=0 add 6 h=6
h+10=0 subtract 10 h=-10 h=-10 or 6
6.subtract 5x from both sides x^2-5x-14=0 find what 2 numbers multiply to get -14 and add to get -5 the numbers are -7 and 2 factor (x-7)(x+2)=0 set each to zero x-7=0 add 7 x=7
x+2=0 subtract 2 x=-2 x=-2 or 7
7.add 2r^2 to both sides 2r^2+11r+15=0 difficult so multiply 2 and 15 and get 30 not factor and find what 2 numbers multiply to get 30 and add to get 11 the numbers are 5 nd 6 split 11 up into 5 and 6 2r^2+6r+5r+15=0 group and factor (2r^2+6r)+(5r+15)=0 factor 2r(r+3)+5(r+3)=0 reverse distribute (2r+5)(r+3)=0 set each to zero 2r+5=0 subtract 5 2r=-5 divide 2 r=-5/2
r+3=0 subtract 3 r=-3 r=-3 or -5/2
8. this is a difference of 2 perfect squares in which if you have x^2-y^2 that factors out of (x-y)(x+y) so x^2-25=0 x^2-5^2=0 (x-5)(x+5)=0 set each to zero x-5=0 add 5 x=5
x+5=0 subtract 5 x=-5 x=-5 or 5
9. differnce of 2 perfect squares 81-4x^2=0 9^2-(2x)^2=0 (9-2x)(9+2x)=0 set each to zero 9-2x=0 add 2x to both sides 9=2x divde 2 9/2=x
9+2x=0 subtract 9 from both sidees 2x=-9 divide 2 x=-9/2 x=-9/2 or 9/2
10. subtract 12s from both sides 4s^2-12s+9=0 multiply 4 and 9 and get 36 find what 2 numbers multiply to get 36 and add to get -12 the numbers are -6 and -6 split up the -12s into -6s and -6s 4s^2-6s-6s+9=0 group (4s^2-6s)+(-6s+9)=0 factor 2s(2s-3)+(-3)(2s-3)=0 reverse distribute (2s-3)(2s-3)=0 set each to zero 2s-3=0 add 3 2s=3 divide 2 s=3/2
ANWERS: 1. x=0 or -7 2. s=-3 or 0 3. x=-4 4. x=5 5. h=-10 or 6 6. x=-2 or 7 7. r=-3 or -5/2 8. x=-5 or 5 9. x=-9/2 or 9/2 10. s=3/2
