12+6x(x+1)=(3x+7)(2x-2)

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Solution for 12+6x(x+1)=(3x+7)(2x-2) equation: 


Simplifying
12 + 6x(x + 1) = (3x + 7)(2x + -2)

Reorder the terms:
12 + 6x(1 + x) = (3x + 7)(2x + -2)
12 + (1 * 6x + x * 6x) = (3x + 7)(2x + -2)
12 + (6x + 6x2) = (3x + 7)(2x + -2)

Reorder the terms:
12 + 6x + 6x2 = (7 + 3x)(2x + -2)

Reorder the terms:
12 + 6x + 6x2 = (7 + 3x)(-2 + 2x)

Multiply (7 + 3x) * (-2 + 2x)
12 + 6x + 6x2 = (7(-2 + 2x) + 3x * (-2 + 2x))
12 + 6x + 6x2 = ((-2 * 7 + 2x * 7) + 3x * (-2 + 2x))
12 + 6x + 6x2 = ((-14 + 14x) + 3x * (-2 + 2x))
12 + 6x + 6x2 = (-14 + 14x + (-2 * 3x + 2x * 3x))
12 + 6x + 6x2 = (-14 + 14x + (-6x + 6x2))

Combine like terms: 14x + -6x = 8x
12 + 6x + 6x2 = (-14 + 8x + 6x2)

Add '-6x2' to each side of the equation.
12 + 6x + 6x2 + -6x2 = -14 + 8x + 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
12 + 6x + 0 = -14 + 8x + 6x2 + -6x2
12 + 6x = -14 + 8x + 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
12 + 6x = -14 + 8x + 0
12 + 6x = -14 + 8x

Solving
12 + 6x = -14 + 8x

Solving for variable 'x'.

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

Add '-8x' to each side of the equation.
12 + 6x + -8x = -14 + 8x + -8x

Combine like terms: 6x + -8x = -2x
12 + -2x = -14 + 8x + -8x

Combine like terms: 8x + -8x = 0
12 + -2x = -14 + 0
12 + -2x = -14

Add '-12' to each side of the equation.
12 + -12 + -2x = -14 + -12

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

Combine like terms: -14 + -12 = -26
-2x = -26

Divide each side by '-2'.
x = 13

Simplifying
x = 13

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