Question

Find the product. (5x² – 4x+6)(–2x+3) = 0

Answer 1

Answer:

x = 3/2

Step-by-step explanation:

Solve for x over the real numbers:

(5 x^2 - 4 x + 6) (3 - 2 x) = 0

Split into two equations:

3 - 2 x = 0 or 5 x^2 - 4 x + 6 = 0

Multiply both sides by -1:

2 x - 3 = 0 or 5 x^2 - 4 x + 6 = 0

Add 3 to both sides:

2 x = 3 or 5 x^2 - 4 x + 6 = 0

Divide both sides by 2:

x = 3/2 or 5 x^2 - 4 x + 6 = 0

Divide both sides by 5:

x = 3/2 or x^2 - (4 x)/5 + 6/5 = 0

Subtract 6/5 from both sides:

x = 3/2 or x^2 - (4 x)/5 = -6/5

Add 4/25 to both sides:

x = 3/2 or x^2 - (4 x)/5 + 4/25 = -26/25

Write the left hand side as a square:

x = 3/2 or (x - 2/5)^2 = -26/25

(x - 2/5)^2 = -26/25 has no solution since for all x on the real line, (x - 2/5)^2 >=0 and -26/25<0:

Answer:  x = 3/2