3x^2+24x-54=6

Solution for 3x^2+24x-54=6 equation:

Simplifying
3x2 + 24x + -54 = 6

Reorder the terms:
-54 + 24x + 3x2 = 6

Solving
-54 + 24x + 3x2 = 6

Solving for variable 'x'.

Reorder the terms:
-54 + -6 + 24x + 3x2 = 6 + -6

Combine like terms: -54 + -6 = -60
-60 + 24x + 3x2 = 6 + -6

Combine like terms: 6 + -6 = 0
-60 + 24x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-20 + 8x + x2) = 0

Factor a trinomial.
3((-10 + -1x)(2 + -1x)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-10 + -1x)' equal to zero and attempt to solve:

Simplifying
-10 + -1x = 0

Solving
-10 + -1x = 0

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

Add '10' to each side of the equation.
-10 + 10 + -1x = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -1x = 0 + 10
-1x = 0 + 10

Combine like terms: 0 + 10 = 10
-1x = 10

Divide each side by '-1'.
x = -10

Simplifying
x = -10
Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-10, 2}