(x+2)(x-5)=(x-7)(x+6)

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Solution for (x+2)(x-5)=(x-7)(x+6) equation: 


Simplifying
(x + 2)(x + -5) = (x + -7)(x + 6)

Reorder the terms:
(2 + x)(x + -5) = (x + -7)(x + 6)

Reorder the terms:
(2 + x)(-5 + x) = (x + -7)(x + 6)

Multiply (2 + x) * (-5 + x)
(2(-5 + x) + x(-5 + x)) = (x + -7)(x + 6)
((-5 * 2 + x * 2) + x(-5 + x)) = (x + -7)(x + 6)
((-10 + 2x) + x(-5 + x)) = (x + -7)(x + 6)
(-10 + 2x + (-5 * x + x * x)) = (x + -7)(x + 6)
(-10 + 2x + (-5x + x2)) = (x + -7)(x + 6)

Combine like terms: 2x + -5x = -3x
(-10 + -3x + x2) = (x + -7)(x + 6)

Reorder the terms:
-10 + -3x + x2 = (-7 + x)(x + 6)

Reorder the terms:
-10 + -3x + x2 = (-7 + x)(6 + x)

Multiply (-7 + x) * (6 + x)
-10 + -3x + x2 = (-7(6 + x) + x(6 + x))
-10 + -3x + x2 = ((6 * -7 + x * -7) + x(6 + x))
-10 + -3x + x2 = ((-42 + -7x) + x(6 + x))
-10 + -3x + x2 = (-42 + -7x + (6 * x + x * x))
-10 + -3x + x2 = (-42 + -7x + (6x + x2))

Combine like terms: -7x + 6x = -1x
-10 + -3x + x2 = (-42 + -1x + x2)

Add '-1x2' to each side of the equation.
-10 + -3x + x2 + -1x2 = -42 + -1x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-10 + -3x + 0 = -42 + -1x + x2 + -1x2
-10 + -3x = -42 + -1x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-10 + -3x = -42 + -1x + 0
-10 + -3x = -42 + -1x

Solving
-10 + -3x = -42 + -1x

Solving for variable 'x'.

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

Add 'x' to each side of the equation.
-10 + -3x + x = -42 + -1x + x

Combine like terms: -3x + x = -2x
-10 + -2x = -42 + -1x + x

Combine like terms: -1x + x = 0
-10 + -2x = -42 + 0
-10 + -2x = -42

Add '10' to each side of the equation.
-10 + 10 + -2x = -42 + 10

Combine like terms: -10 + 10 = 0
0 + -2x = -42 + 10
-2x = -42 + 10

Combine like terms: -42 + 10 = -32
-2x = -32

Divide each side by '-2'.
x = 16

Simplifying
x = 16

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