Question

Solve the quadratic equation by factoring and show work: 6x²−x=15

Answer 1

Answer:

$x_{1} = -\frac{3}{2} \\x_{2}=\frac{5}{3}$

Step-by-step explanation:

$6x^{2} -x=15$ move the constant to the left

$6x^{2} -x-15=0$ write as a difference

$6x^{2} +9x-10x-15=0$ factor the expressions

$3x *(2x+3)-5(2x+3)=0$ factor the expression

$(2x+3) * (3x-5) = 0$ split into possible cases

$2x+3=0\\3x-5=0$ solve the equations

Answer 2

Answer:

$(2x + 3)(3x - 5)$

Step-by-step explanation:

Step 1:  Subtract 15 from both sides

$6x^2 - x - 15 = 15 - 15$

$6x^2 - x - 15$

Step 2:  Factor

$6x^2 - x - 15$

$(2x + 3)(3x - 5)$

Answer:  $(2x + 3)(3x - 5)$