(x+7)(x-8)-(x-9)(x+10)=0

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Solution for (x+7)(x-8)-(x-9)(x+10)=0 equation: 


Simplifying
(x + 7)(x + -8) + -1(x + -9)(x + 10) = 0

Reorder the terms:
(7 + x)(x + -8) + -1(x + -9)(x + 10) = 0

Reorder the terms:
(7 + x)(-8 + x) + -1(x + -9)(x + 10) = 0

Multiply (7 + x) * (-8 + x)
(7(-8 + x) + x(-8 + x)) + -1(x + -9)(x + 10) = 0
((-8 * 7 + x * 7) + x(-8 + x)) + -1(x + -9)(x + 10) = 0
((-56 + 7x) + x(-8 + x)) + -1(x + -9)(x + 10) = 0
(-56 + 7x + (-8 * x + x * x)) + -1(x + -9)(x + 10) = 0
(-56 + 7x + (-8x + x2)) + -1(x + -9)(x + 10) = 0

Combine like terms: 7x + -8x = -1x
(-56 + -1x + x2) + -1(x + -9)(x + 10) = 0

Reorder the terms:
-56 + -1x + x2 + -1(-9 + x)(x + 10) = 0

Reorder the terms:
-56 + -1x + x2 + -1(-9 + x)(10 + x) = 0

Multiply (-9 + x) * (10 + x)
-56 + -1x + x2 + -1(-9(10 + x) + x(10 + x)) = 0
-56 + -1x + x2 + -1((10 * -9 + x * -9) + x(10 + x)) = 0
-56 + -1x + x2 + -1((-90 + -9x) + x(10 + x)) = 0
-56 + -1x + x2 + -1(-90 + -9x + (10 * x + x * x)) = 0
-56 + -1x + x2 + -1(-90 + -9x + (10x + x2)) = 0

Combine like terms: -9x + 10x = 1x
-56 + -1x + x2 + -1(-90 + 1x + x2) = 0
-56 + -1x + x2 + (-90 * -1 + 1x * -1 + x2 * -1) = 0
-56 + -1x + x2 + (90 + -1x + -1x2) = 0

Reorder the terms:
-56 + 90 + -1x + -1x + x2 + -1x2 = 0

Combine like terms: -56 + 90 = 34
34 + -1x + -1x + x2 + -1x2 = 0

Combine like terms: -1x + -1x = -2x
34 + -2x + x2 + -1x2 = 0

Combine like terms: x2 + -1x2 = 0
34 + -2x + 0 = 0
34 + -2x = 0

Solving
34 + -2x = 0

Solving for variable 'x'.

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

Add '-34' to each side of the equation.
34 + -34 + -2x = 0 + -34

Combine like terms: 34 + -34 = 0
0 + -2x = 0 + -34
-2x = 0 + -34

Combine like terms: 0 + -34 = -34
-2x = -34

Divide each side by '-2'.
x = 17

Simplifying
x = 17

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