4x=2(3x+1)-12x(x)

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Solution for 4x=2(3x+1)-12x(x) equation: 


Simplifying
4x = 2(3x + 1) + -12x(x)

Reorder the terms:
4x = 2(1 + 3x) + -12x(x)
4x = (1 * 2 + 3x * 2) + -12x(x)
4x = (2 + 6x) + -12x(x)

Multiply x * x
4x = 2 + 6x + -12x2

Solving
4x = 2 + 6x + -12x2

Solving for variable 'x'.

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

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

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

Combine like terms: 2 + -2 = 0
-2 + -2x + 12x2 = 0 + 6x + -6x + -12x2 + 12x2
-2 + -2x + 12x2 = 6x + -6x + -12x2 + 12x2

Combine like terms: 6x + -6x = 0
-2 + -2x + 12x2 = 0 + -12x2 + 12x2
-2 + -2x + 12x2 = -12x2 + 12x2

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

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + -1x + 6x2) = 0

Factor a trinomial.
2((-1 + -3x)(1 + -2x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-1 + -3x)' equal to zero and attempt to solve:

Simplifying
-1 + -3x = 0

Solving
-1 + -3x = 0

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

Add '1' to each side of the equation.
-1 + 1 + -3x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -3x = 0 + 1
-3x = 0 + 1

Combine like terms: 0 + 1 = 1
-3x = 1

Divide each side by '-3'.
x = -0.3333333333

Simplifying
x = -0.3333333333

Subproblem 2
Set the factor '(1 + -2x)' equal to zero and attempt to solve:

Simplifying
1 + -2x = 0

Solving
1 + -2x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -2x = 0 + -1

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

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

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5
Solution
x = {-0.3333333333, 0.5}

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