2(x+3)-6(x-1)=4(2x+2)-5(x-5)

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Solution for 2(x+3)-6(x-1)=4(2x+2)-5(x-5) equation: 


Simplifying
2(x + 3) + -6(x + -1) = 4(2x + 2) + -5(x + -5)

Reorder the terms:
2(3 + x) + -6(x + -1) = 4(2x + 2) + -5(x + -5)
(3 * 2 + x * 2) + -6(x + -1) = 4(2x + 2) + -5(x + -5)
(6 + 2x) + -6(x + -1) = 4(2x + 2) + -5(x + -5)

Reorder the terms:
6 + 2x + -6(-1 + x) = 4(2x + 2) + -5(x + -5)
6 + 2x + (-1 * -6 + x * -6) = 4(2x + 2) + -5(x + -5)
6 + 2x + (6 + -6x) = 4(2x + 2) + -5(x + -5)

Reorder the terms:
6 + 6 + 2x + -6x = 4(2x + 2) + -5(x + -5)

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

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

Reorder the terms:
12 + -4x = 4(2 + 2x) + -5(x + -5)
12 + -4x = (2 * 4 + 2x * 4) + -5(x + -5)
12 + -4x = (8 + 8x) + -5(x + -5)

Reorder the terms:
12 + -4x = 8 + 8x + -5(-5 + x)
12 + -4x = 8 + 8x + (-5 * -5 + x * -5)
12 + -4x = 8 + 8x + (25 + -5x)

Reorder the terms:
12 + -4x = 8 + 25 + 8x + -5x

Combine like terms: 8 + 25 = 33
12 + -4x = 33 + 8x + -5x

Combine like terms: 8x + -5x = 3x
12 + -4x = 33 + 3x

Solving
12 + -4x = 33 + 3x

Solving for variable 'x'.

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

Add '-3x' to each side of the equation.
12 + -4x + -3x = 33 + 3x + -3x

Combine like terms: -4x + -3x = -7x
12 + -7x = 33 + 3x + -3x

Combine like terms: 3x + -3x = 0
12 + -7x = 33 + 0
12 + -7x = 33

Add '-12' to each side of the equation.
12 + -12 + -7x = 33 + -12

Combine like terms: 12 + -12 = 0
0 + -7x = 33 + -12
-7x = 33 + -12

Combine like terms: 33 + -12 = 21
-7x = 21

Divide each side by '-7'.
x = -3

Simplifying
x = -3

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