12x^2=27x+27

Solution for 12x^2=27x+27 equation:

Simplifying
12x2 = 27x + 27

Reorder the terms:
12x2 = 27 + 27x

Solving
12x2 = 27 + 27x

Solving for variable 'x'.

Reorder the terms:
-27 + -27x + 12x2 = 27 + 27x + -27 + -27x

Reorder the terms:
-27 + -27x + 12x2 = 27 + -27 + 27x + -27x

Combine like terms: 27 + -27 = 0
-27 + -27x + 12x2 = 0 + 27x + -27x
-27 + -27x + 12x2 = 27x + -27x

Combine like terms: 27x + -27x = 0
-27 + -27x + 12x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-9 + -9x + 4x2) = 0

Factor a trinomial.
3((-3 + -4x)(3 + -1x)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-3 + -4x)' equal to zero and attempt to solve:

Simplifying
-3 + -4x = 0

Solving
-3 + -4x = 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 + -4x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -4x = 0 + 3
-4x = 0 + 3

Combine like terms: 0 + 3 = 3
-4x = 3

Divide each side by '-4'.
x = -0.75

Simplifying
x = -0.75
Subproblem 2
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
Solution
x = {-0.75, 3}