Question

Use the zero product property to find the solutions to the equation 6x2 – 5x = 56.
x = –8 or x = 7/6
x = -8/3 or x =7/2
x = -1/2 or x = 56/3
x = -3/7 or x = 2/3

Answer 1

Start with 6x^2 − 5x = 56. Move 56 to the left:
6x^2 − 5x − 56 = 0.

Factor:
6x^2 − 21x + 16x − 56 = 0
3x(2x − 7) + 8(2x − 7) = 0
(2x − 7)(3x + 8) = 0.

By the zero-product property, 2x − 7 = 0 or 3x + 8 = 0, so
x = 7/2 or x = −8/3.