(2x-2)(7x+8)=0

Solution for (2x-2)(7x+8)=0 equation:

Simplifying
(2x + -2)(7x + 8) = 0

Reorder the terms:
(-2 + 2x)(7x + 8) = 0

Reorder the terms:
(-2 + 2x)(8 + 7x) = 0

Multiply (-2 + 2x) * (8 + 7x)
(-2(8 + 7x) + 2x * (8 + 7x)) = 0
((8 * -2 + 7x * -2) + 2x * (8 + 7x)) = 0
((-16 + -14x) + 2x * (8 + 7x)) = 0
(-16 + -14x + (8 * 2x + 7x * 2x)) = 0
(-16 + -14x + (16x + 14x2)) = 0

Combine like terms: -14x + 16x = 2x
(-16 + 2x + 14x2) = 0

Solving
-16 + 2x + 14x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-8 + x + 7x2) = 0

Factor a trinomial.
2((-8 + -7x)(1 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-8 + -7x)' equal to zero and attempt to solve:

Simplifying
-8 + -7x = 0

Solving
-8 + -7x = 0

Move all terms containing x to the left, all other terms to the right.

Add '8' to each side of the equation.
-8 + 8 + -7x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -7x = 0 + 8
-7x = 0 + 8

Combine like terms: 0 + 8 = 8
-7x = 8

Divide each side by '-7'.
x = -1.142857143

Simplifying
x = -1.142857143
Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + -1x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1x = 0 + -1
-1x = 0 + -1

Combine like terms: 0 + -1 = -1
-1x = -1

Divide each side by '-1'.
x = 1

Simplifying
x = 1
Solution
x = {-1.142857143, 1}