6x^2+12x+36=54

Solution for 6x^2+12x+36=54 equation:

Simplifying
6x2 + 12x + 36 = 54

Reorder the terms:
36 + 12x + 6x2 = 54

Solving
36 + 12x + 6x2 = 54

Solving for variable 'x'.

Reorder the terms:
36 + -54 + 12x + 6x2 = 54 + -54

Combine like terms: 36 + -54 = -18
-18 + 12x + 6x2 = 54 + -54

Combine like terms: 54 + -54 = 0
-18 + 12x + 6x2 = 0

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

Factor a trinomial.
6((-3 + -1x)(1 + -1x)) = 0

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

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1x = 0 + 3
-1x = 0 + 3

Combine like terms: 0 + 3 = 3
-1x = 3

Divide each side by '-1'.
x = -3

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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 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 + -1x = 0 + -1

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

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

Divide each side by '-1'.
x = 1

Simplifying
x = 1
Solution
x = {-3, 1}