6x(3x+5)=-6+12x

Solution for 6x(3x+5)=-6+12x equation:

Simplifying
6x(3x + 5) = -6 + 12x

Reorder the terms:
6x(5 + 3x) = -6 + 12x
(5 * 6x + 3x * 6x) = -6 + 12x
(30x + 18x2) = -6 + 12x

Solving
30x + 18x2 = -6 + 12x

Solving for variable 'x'.

Reorder the terms:
6 + 30x + -12x + 18x2 = -6 + 12x + 6 + -12x

Combine like terms: 30x + -12x = 18x
6 + 18x + 18x2 = -6 + 12x + 6 + -12x

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

Combine like terms: -6 + 6 = 0
6 + 18x + 18x2 = 0 + 12x + -12x
6 + 18x + 18x2 = 12x + -12x

Combine like terms: 12x + -12x = 0
6 + 18x + 18x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(1 + 3x + 3x2) = 0

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

Simplifying
1 + 3x + 3x2 = 0

Solving
1 + 3x + 3x2 = 0

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

Divide each side by '3'.
0.3333333333 + x + x2 = 0

Move the constant term to the right:

Add '-0.3333333333' to each side of the equation.
0.3333333333 + x + -0.3333333333 + x2 = 0 + -0.3333333333

Reorder the terms:
0.3333333333 + -0.3333333333 + x + x2 = 0 + -0.3333333333

Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000
0.0000000000 + x + x2 = 0 + -0.3333333333
x + x2 = 0 + -0.3333333333

Combine like terms: 0 + -0.3333333333 = -0.3333333333
x + x2 = -0.3333333333

The x term is x.  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.
 + 0.25 + x2 = -0.3333333333 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + x2 = -0.3333333333 + 0.25

Combine like terms: -0.3333333333 + 0.25 = -0.0833333333
1.25 + x2 = -0.0833333333

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = -0.0833333333

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.