(x-7)(x+2)=(x-5)(x-7)

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Solution for (x-7)(x+2)=(x-5)(x-7) equation: 


Simplifying
(x + -7)(x + 2) = (x + -5)(x + -7)

Reorder the terms:
(-7 + x)(x + 2) = (x + -5)(x + -7)

Reorder the terms:
(-7 + x)(2 + x) = (x + -5)(x + -7)

Multiply (-7 + x) * (2 + x)
(-7(2 + x) + x(2 + x)) = (x + -5)(x + -7)
((2 * -7 + x * -7) + x(2 + x)) = (x + -5)(x + -7)
((-14 + -7x) + x(2 + x)) = (x + -5)(x + -7)
(-14 + -7x + (2 * x + x * x)) = (x + -5)(x + -7)
(-14 + -7x + (2x + x2)) = (x + -5)(x + -7)

Combine like terms: -7x + 2x = -5x
(-14 + -5x + x2) = (x + -5)(x + -7)

Reorder the terms:
-14 + -5x + x2 = (-5 + x)(x + -7)

Reorder the terms:
-14 + -5x + x2 = (-5 + x)(-7 + x)

Multiply (-5 + x) * (-7 + x)
-14 + -5x + x2 = (-5(-7 + x) + x(-7 + x))
-14 + -5x + x2 = ((-7 * -5 + x * -5) + x(-7 + x))
-14 + -5x + x2 = ((35 + -5x) + x(-7 + x))
-14 + -5x + x2 = (35 + -5x + (-7 * x + x * x))
-14 + -5x + x2 = (35 + -5x + (-7x + x2))

Combine like terms: -5x + -7x = -12x
-14 + -5x + x2 = (35 + -12x + x2)

Add '-1x2' to each side of the equation.
-14 + -5x + x2 + -1x2 = 35 + -12x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-14 + -5x + 0 = 35 + -12x + x2 + -1x2
-14 + -5x = 35 + -12x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-14 + -5x = 35 + -12x + 0
-14 + -5x = 35 + -12x

Solving
-14 + -5x = 35 + -12x

Solving for variable 'x'.

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

Add '12x' to each side of the equation.
-14 + -5x + 12x = 35 + -12x + 12x

Combine like terms: -5x + 12x = 7x
-14 + 7x = 35 + -12x + 12x

Combine like terms: -12x + 12x = 0
-14 + 7x = 35 + 0
-14 + 7x = 35

Add '14' to each side of the equation.
-14 + 14 + 7x = 35 + 14

Combine like terms: -14 + 14 = 0
0 + 7x = 35 + 14
7x = 35 + 14

Combine like terms: 35 + 14 = 49
7x = 49

Divide each side by '7'.
x = 7

Simplifying
x = 7

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