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

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

Simplifying
6x(3 + x) = 12x + -12
(3 * 6x + x * 6x) = 12x + -12
(18x + 6x2) = 12x + -12

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

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

Solving for variable 'x'.

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

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

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

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

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

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

Ignore the factor 6.
Subproblem 1
Set the factor '(2 + x + x2)' equal to zero and attempt to solve:

Simplifying
2 + x + x2 = 0

Solving
2 + x + x2 = 0

Begin completing the square.

Move the constant term to the right:

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

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

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

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

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.
x + 0.25 + x2 = -2 + 0.25

Reorder the terms:
0.25 + x + x2 = -2 + 0.25

Combine like terms: -2 + 0.25 = -1.75
0.25 + x + x2 = -1.75

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = -1.75

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.