(6-2x)3x=4x+12

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Solution for (6-2x)3x=4x+12 equation: 


Simplifying
(6 + -2x) * 3x = 4x + 12

Reorder the terms for easier multiplication:
3x(6 + -2x) = 4x + 12
(6 * 3x + -2x * 3x) = 4x + 12
(18x + -6x2) = 4x + 12

Reorder the terms:
18x + -6x2 = 12 + 4x

Solving
18x + -6x2 = 12 + 4x

Solving for variable 'x'.

Reorder the terms:
-12 + 18x + -4x + -6x2 = 12 + 4x + -12 + -4x

Combine like terms: 18x + -4x = 14x
-12 + 14x + -6x2 = 12 + 4x + -12 + -4x

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

Combine like terms: 12 + -12 = 0
-12 + 14x + -6x2 = 0 + 4x + -4x
-12 + 14x + -6x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
-12 + 14x + -6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-6 + 7x + -3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-6 + 7x + -3x2)' equal to zero and attempt to solve:

Simplifying
-6 + 7x + -3x2 = 0

Solving
-6 + 7x + -3x2 = 0

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
2 + -2.333333333x + x2 = 0

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + -2.333333333x + -2 + x2 = 0 + -2

Reorder the terms:
2 + -2 + -2.333333333x + x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -2.333333333x + x2 = 0 + -2
-2.333333333x + x2 = 0 + -2

Combine like terms: 0 + -2 = -2
-2.333333333x + x2 = -2

The x term is -2.333333333x.  Take half its coefficient (-1.166666667).
Square it (1.361111112) and add it to both sides.

Add '1.361111112' to each side of the equation.
-2.333333333x + 1.361111112 + x2 = -2 + 1.361111112

Reorder the terms:
1.361111112 + -2.333333333x + x2 = -2 + 1.361111112

Combine like terms: -2 + 1.361111112 = -0.638888888
1.361111112 + -2.333333333x + x2 = -0.638888888

Factor a perfect square on the left side:
(x + -1.166666667)(x + -1.166666667) = -0.638888888

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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