(x-8)(x+9)+(x-8)(x+7)=0

Solution for (x-8)(x+9)+(x-8)(x+7)=0 equation:

Simplifying
(x + -8)(x + 9) + (x + -8)(x + 7) = 0

Reorder the terms:
(-8 + x)(x + 9) + (x + -8)(x + 7) = 0

Reorder the terms:
(-8 + x)(9 + x) + (x + -8)(x + 7) = 0

Multiply (-8 + x) * (9 + x)
(-8(9 + x) + x(9 + x)) + (x + -8)(x + 7) = 0
((9 * -8 + x * -8) + x(9 + x)) + (x + -8)(x + 7) = 0
((-72 + -8x) + x(9 + x)) + (x + -8)(x + 7) = 0
(-72 + -8x + (9 * x + x * x)) + (x + -8)(x + 7) = 0
(-72 + -8x + (9x + x2)) + (x + -8)(x + 7) = 0

Combine like terms: -8x + 9x = 1x
(-72 + 1x + x2) + (x + -8)(x + 7) = 0

Reorder the terms:
-72 + 1x + x2 + (-8 + x)(x + 7) = 0

Reorder the terms:
-72 + 1x + x2 + (-8 + x)(7 + x) = 0

Multiply (-8 + x) * (7 + x)
-72 + 1x + x2 + (-8(7 + x) + x(7 + x)) = 0
-72 + 1x + x2 + ((7 * -8 + x * -8) + x(7 + x)) = 0
-72 + 1x + x2 + ((-56 + -8x) + x(7 + x)) = 0
-72 + 1x + x2 + (-56 + -8x + (7 * x + x * x)) = 0
-72 + 1x + x2 + (-56 + -8x + (7x + x2)) = 0

Combine like terms: -8x + 7x = -1x
-72 + 1x + x2 + (-56 + -1x + x2) = 0

Reorder the terms:
-72 + -56 + 1x + -1x + x2 + x2 = 0

Combine like terms: -72 + -56 = -128
-128 + 1x + -1x + x2 + x2 = 0

Combine like terms: 1x + -1x = 0
-128 + 0 + x2 + x2 = 0
-128 + x2 + x2 = 0

Combine like terms: x2 + x2 = 2x2
-128 + 2x2 = 0

Solving
-128 + 2x2 = 0

Solving for variable 'x'.

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

Add '128' to each side of the equation.
-128 + 128 + 2x2 = 0 + 128

Combine like terms: -128 + 128 = 0
0 + 2x2 = 0 + 128
2x2 = 0 + 128

Combine like terms: 0 + 128 = 128
2x2 = 128

Divide each side by '2'.
x2 = 64

Simplifying
x2 = 64

Take the square root of each side:
x = {-8, 8}