6x^2=-6(2x+1)

Solution for 6x^2=-6(2x+1) equation:

Simplifying
6x2 = -6(2x + 1)

Reorder the terms:
6x2 = -6(1 + 2x)
6x2 = (1 * -6 + 2x * -6)
6x2 = (-6 + -12x)

Solving
6x2 = -6 + -12x

Solving for variable 'x'.

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

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

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

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

Factor out the Greatest Common Factor (GCF), '6'.
6(1 + 2x + x2) = 0

Factor a trinomial.
6((1 + x)(1 + x)) = 0

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

Simplifying
1 + x = 0

Solving
1 + x = 0

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

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

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

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

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

Simplifying
1 + x = 0

Solving
1 + x = 0

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

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

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

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

Simplifying
x = -1
Solution
x = {-1, -1}