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

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

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

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

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

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

Solving for variable 'x'.

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

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

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

Combine like terms: 6 + -6 = 0
-6 + 18x + 4x2 = 0 + -12x + 12x
-6 + 18x + 4x2 = -12x + 12x

Combine like terms: -12x + 12x = 0
-6 + 18x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + 9x + 2x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-3 + 9x + 2x2)' equal to zero and attempt to solve:

Simplifying
-3 + 9x + 2x2 = 0

Solving
-3 + 9x + 2x2 = 0

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

Divide each side by '2'.
-1.5 + 4.5x + x2 = 0

Move the constant term to the right:

Add '1.5' to each side of the equation.
-1.5 + 4.5x + 1.5 + x2 = 0 + 1.5

Reorder the terms:
-1.5 + 1.5 + 4.5x + x2 = 0 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + 4.5x + x2 = 0 + 1.5
4.5x + x2 = 0 + 1.5

Combine like terms: 0 + 1.5 = 1.5
4.5x + x2 = 1.5

The x term is 4.5x.  Take half its coefficient (2.25).
Square it (5.0625) and add it to both sides.

Add '5.0625' to each side of the equation.
4.5x + 5.0625 + x2 = 1.5 + 5.0625

Reorder the terms:
5.0625 + 4.5x + x2 = 1.5 + 5.0625

Combine like terms: 1.5 + 5.0625 = 6.5625
5.0625 + 4.5x + x2 = 6.5625

Factor a perfect square on the left side:
(x + 2.25)(x + 2.25) = 6.5625

Calculate the square root of the right side: 2.561737691

Break this problem into two subproblems by setting 
(x + 2.25) equal to 2.561737691 and -2.561737691.

Subproblem 1
x + 2.25 = 2.561737691

Simplifying
x + 2.25 = 2.561737691

Reorder the terms:
2.25 + x = 2.561737691

Solving
2.25 + x = 2.561737691

Solving for variable 'x'.

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

Add '-2.25' to each side of the equation.
2.25 + -2.25 + x = 2.561737691 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + x = 2.561737691 + -2.25
x = 2.561737691 + -2.25

Combine like terms: 2.561737691 + -2.25 = 0.311737691
x = 0.311737691

Simplifying
x = 0.311737691

Subproblem 2
x + 2.25 = -2.561737691

Simplifying
x + 2.25 = -2.561737691

Reorder the terms:
2.25 + x = -2.561737691

Solving
2.25 + x = -2.561737691

Solving for variable 'x'.

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

Add '-2.25' to each side of the equation.
2.25 + -2.25 + x = -2.561737691 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + x = -2.561737691 + -2.25
x = -2.561737691 + -2.25

Combine like terms: -2.561737691 + -2.25 = -4.811737691
x = -4.811737691

Simplifying
x = -4.811737691

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.311737691, -4.811737691}
Solution
x = {0.311737691, -4.811737691}