12-6x(x+4)+10x=2x+2(2x+6)

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Solution for 12-6x(x+4)+10x=2x+2(2x+6) equation: 


Simplifying
12 + -6x(x + 4) + 10x = 2x + 2(2x + 6)

Reorder the terms:
12 + -6x(4 + x) + 10x = 2x + 2(2x + 6)
12 + (4 * -6x + x * -6x) + 10x = 2x + 2(2x + 6)
12 + (-24x + -6x2) + 10x = 2x + 2(2x + 6)

Reorder the terms:
12 + -24x + 10x + -6x2 = 2x + 2(2x + 6)

Combine like terms: -24x + 10x = -14x
12 + -14x + -6x2 = 2x + 2(2x + 6)

Reorder the terms:
12 + -14x + -6x2 = 2x + 2(6 + 2x)
12 + -14x + -6x2 = 2x + (6 * 2 + 2x * 2)
12 + -14x + -6x2 = 2x + (12 + 4x)

Reorder the terms:
12 + -14x + -6x2 = 12 + 2x + 4x

Combine like terms: 2x + 4x = 6x
12 + -14x + -6x2 = 12 + 6x

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

Reorder the terms:
12 + -12 + -14x + -6x2 = 12 + -12 + 6x

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

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

Solving
-14x + -6x2 = 6x

Solving for variable 'x'.

Reorder the terms:
-14x + -6x + -6x2 = 6x + -6x

Combine like terms: -14x + -6x = -20x
-20x + -6x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
-20x + -6x2 = 0

Factor out the Greatest Common Factor (GCF), '-2x'.
-2x(10 + 3x) = 0

Ignore the factor -2.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(10 + 3x)' equal to zero and attempt to solve:

Simplifying
10 + 3x = 0

Solving
10 + 3x = 0

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

Add '-10' to each side of the equation.
10 + -10 + 3x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + 3x = 0 + -10
3x = 0 + -10

Combine like terms: 0 + -10 = -10
3x = -10

Divide each side by '3'.
x = -3.333333333

Simplifying
x = -3.333333333
Solution
x = {0, -3.333333333}

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