6x^2-24x-27=3

Solution for 6x^2-24x-27=3 equation:

Simplifying
6x2 + -24x + -27 = 3

Reorder the terms:
-27 + -24x + 6x2 = 3

Solving
-27 + -24x + 6x2 = 3

Solving for variable 'x'.

Reorder the terms:
-27 + -3 + -24x + 6x2 = 3 + -3

Combine like terms: -27 + -3 = -30
-30 + -24x + 6x2 = 3 + -3

Combine like terms: 3 + -3 = 0
-30 + -24x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-5 + -4x + x2) = 0

Factor a trinomial.
6((-1 + -1x)(5 + -1x)) = 0

Ignore the factor 6.
Subproblem 1
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
Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-1, 5}