(x-2)(x+6)=(x+3)(x-5)

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Solution for (x-2)(x+6)=(x+3)(x-5) equation: 


Simplifying
(x + -2)(x + 6) = (x + 3)(x + -5)

Reorder the terms:
(-2 + x)(x + 6) = (x + 3)(x + -5)

Reorder the terms:
(-2 + x)(6 + x) = (x + 3)(x + -5)

Multiply (-2 + x) * (6 + x)
(-2(6 + x) + x(6 + x)) = (x + 3)(x + -5)
((6 * -2 + x * -2) + x(6 + x)) = (x + 3)(x + -5)
((-12 + -2x) + x(6 + x)) = (x + 3)(x + -5)
(-12 + -2x + (6 * x + x * x)) = (x + 3)(x + -5)
(-12 + -2x + (6x + x2)) = (x + 3)(x + -5)

Combine like terms: -2x + 6x = 4x
(-12 + 4x + x2) = (x + 3)(x + -5)

Reorder the terms:
-12 + 4x + x2 = (3 + x)(x + -5)

Reorder the terms:
-12 + 4x + x2 = (3 + x)(-5 + x)

Multiply (3 + x) * (-5 + x)
-12 + 4x + x2 = (3(-5 + x) + x(-5 + x))
-12 + 4x + x2 = ((-5 * 3 + x * 3) + x(-5 + x))
-12 + 4x + x2 = ((-15 + 3x) + x(-5 + x))
-12 + 4x + x2 = (-15 + 3x + (-5 * x + x * x))
-12 + 4x + x2 = (-15 + 3x + (-5x + x2))

Combine like terms: 3x + -5x = -2x
-12 + 4x + x2 = (-15 + -2x + x2)

Add '-1x2' to each side of the equation.
-12 + 4x + x2 + -1x2 = -15 + -2x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-12 + 4x + 0 = -15 + -2x + x2 + -1x2
-12 + 4x = -15 + -2x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-12 + 4x = -15 + -2x + 0
-12 + 4x = -15 + -2x

Solving
-12 + 4x = -15 + -2x

Solving for variable 'x'.

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

Add '2x' to each side of the equation.
-12 + 4x + 2x = -15 + -2x + 2x

Combine like terms: 4x + 2x = 6x
-12 + 6x = -15 + -2x + 2x

Combine like terms: -2x + 2x = 0
-12 + 6x = -15 + 0
-12 + 6x = -15

Add '12' to each side of the equation.
-12 + 12 + 6x = -15 + 12

Combine like terms: -12 + 12 = 0
0 + 6x = -15 + 12
6x = -15 + 12

Combine like terms: -15 + 12 = -3
6x = -3

Divide each side by '6'.
x = -0.5

Simplifying
x = -0.5

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