(x+1)(x-5)=(x+2)(x-7)

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Solution for (x+1)(x-5)=(x+2)(x-7) equation: 


Simplifying
(x + 1)(x + -5) = (x + 2)(x + -7)

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

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

Multiply (1 + x) * (-5 + x)
(1(-5 + x) + x(-5 + x)) = (x + 2)(x + -7)
((-5 * 1 + x * 1) + x(-5 + x)) = (x + 2)(x + -7)
((-5 + 1x) + x(-5 + x)) = (x + 2)(x + -7)
(-5 + 1x + (-5 * x + x * x)) = (x + 2)(x + -7)
(-5 + 1x + (-5x + x2)) = (x + 2)(x + -7)

Combine like terms: 1x + -5x = -4x
(-5 + -4x + x2) = (x + 2)(x + -7)

Reorder the terms:
-5 + -4x + x2 = (2 + x)(x + -7)

Reorder the terms:
-5 + -4x + x2 = (2 + x)(-7 + x)

Multiply (2 + x) * (-7 + x)
-5 + -4x + x2 = (2(-7 + x) + x(-7 + x))
-5 + -4x + x2 = ((-7 * 2 + x * 2) + x(-7 + x))
-5 + -4x + x2 = ((-14 + 2x) + x(-7 + x))
-5 + -4x + x2 = (-14 + 2x + (-7 * x + x * x))
-5 + -4x + x2 = (-14 + 2x + (-7x + x2))

Combine like terms: 2x + -7x = -5x
-5 + -4x + x2 = (-14 + -5x + x2)

Add '-1x2' to each side of the equation.
-5 + -4x + x2 + -1x2 = -14 + -5x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-5 + -4x + 0 = -14 + -5x + x2 + -1x2
-5 + -4x = -14 + -5x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-5 + -4x = -14 + -5x + 0
-5 + -4x = -14 + -5x

Solving
-5 + -4x = -14 + -5x

Solving for variable 'x'.

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

Add '5x' to each side of the equation.
-5 + -4x + 5x = -14 + -5x + 5x

Combine like terms: -4x + 5x = 1x
-5 + 1x = -14 + -5x + 5x

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

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

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

Combine like terms: -14 + 5 = -9
1x = -9

Divide each side by '1'.
x = -9

Simplifying
x = -9

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