12x=12x^2+18

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Solution for 12x=12x^2+18 equation: 


Simplifying
12x = 12x2 + 18

Reorder the terms:
12x = 18 + 12x2

Solving
12x = 18 + 12x2

Solving for variable 'x'.

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

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

Combine like terms: 18 + -18 = 0
-18 + 12x + -12x2 = 0 + 12x2 + -12x2
-18 + 12x + -12x2 = 12x2 + -12x2

Combine like terms: 12x2 + -12x2 = 0
-18 + 12x + -12x2 = 0

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

Ignore the factor 6.

Subproblem 1
Set the factor '(-3 + 2x + -2x2)' equal to zero and attempt to solve:

Simplifying
-3 + 2x + -2x2 = 0

Solving
-3 + 2x + -2x2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
1.5 + -1x + x2 = 0

Move the constant term to the right:

Add '-1.5' to each side of the equation.
1.5 + -1x + -1.5 + x2 = 0 + -1.5

Reorder the terms:
1.5 + -1.5 + -1x + x2 = 0 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + -1x + x2 = 0 + -1.5
-1x + x2 = 0 + -1.5

Combine like terms: 0 + -1.5 = -1.5
-1x + x2 = -1.5

The x term is -1x.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = -1.5 + 0.25

Reorder the terms:
0.25 + -1x + x2 = -1.5 + 0.25

Combine like terms: -1.5 + 0.25 = -1.25
0.25 + -1x + x2 = -1.25

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = -1.25

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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