3x^2+27x=-24

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

Simplifying
3x2 + 27x = -24

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

Solving
27x + 3x2 = -24

Solving for variable 'x'.

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

Combine like terms: -24 + 24 = 0
24 + 27x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(8 + 9x + x2) = 0

Factor a trinomial.
3((8 + x)(1 + x)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(8 + x)' equal to zero and attempt to solve:

Simplifying
8 + x = 0

Solving
8 + x = 0

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

Add '-8' to each side of the equation.
8 + -8 + x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + x = 0 + -8
x = 0 + -8

Combine like terms: 0 + -8 = -8
x = -8

Simplifying
x = -8
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 = {-8, -1}