(x-7)(x-5)-(x-5)(x+7)=0

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Solution for (x-7)(x-5)-(x-5)(x+7)=0 equation: 


Simplifying
(x + -7)(x + -5) + -1(x + -5)(x + 7) = 0

Reorder the terms:
(-7 + x)(x + -5) + -1(x + -5)(x + 7) = 0

Reorder the terms:
(-7 + x)(-5 + x) + -1(x + -5)(x + 7) = 0

Multiply (-7 + x) * (-5 + x)
(-7(-5 + x) + x(-5 + x)) + -1(x + -5)(x + 7) = 0
((-5 * -7 + x * -7) + x(-5 + x)) + -1(x + -5)(x + 7) = 0
((35 + -7x) + x(-5 + x)) + -1(x + -5)(x + 7) = 0
(35 + -7x + (-5 * x + x * x)) + -1(x + -5)(x + 7) = 0
(35 + -7x + (-5x + x2)) + -1(x + -5)(x + 7) = 0

Combine like terms: -7x + -5x = -12x
(35 + -12x + x2) + -1(x + -5)(x + 7) = 0

Reorder the terms:
35 + -12x + x2 + -1(-5 + x)(x + 7) = 0

Reorder the terms:
35 + -12x + x2 + -1(-5 + x)(7 + x) = 0

Multiply (-5 + x) * (7 + x)
35 + -12x + x2 + -1(-5(7 + x) + x(7 + x)) = 0
35 + -12x + x2 + -1((7 * -5 + x * -5) + x(7 + x)) = 0
35 + -12x + x2 + -1((-35 + -5x) + x(7 + x)) = 0
35 + -12x + x2 + -1(-35 + -5x + (7 * x + x * x)) = 0
35 + -12x + x2 + -1(-35 + -5x + (7x + x2)) = 0

Combine like terms: -5x + 7x = 2x
35 + -12x + x2 + -1(-35 + 2x + x2) = 0
35 + -12x + x2 + (-35 * -1 + 2x * -1 + x2 * -1) = 0
35 + -12x + x2 + (35 + -2x + -1x2) = 0

Reorder the terms:
35 + 35 + -12x + -2x + x2 + -1x2 = 0

Combine like terms: 35 + 35 = 70
70 + -12x + -2x + x2 + -1x2 = 0

Combine like terms: -12x + -2x = -14x
70 + -14x + x2 + -1x2 = 0

Combine like terms: x2 + -1x2 = 0
70 + -14x + 0 = 0
70 + -14x = 0

Solving
70 + -14x = 0

Solving for variable 'x'.

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

Add '-70' to each side of the equation.
70 + -70 + -14x = 0 + -70

Combine like terms: 70 + -70 = 0
0 + -14x = 0 + -70
-14x = 0 + -70

Combine like terms: 0 + -70 = -70
-14x = -70

Divide each side by '-14'.
x = 5

Simplifying
x = 5

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