5x^2+51x+108=0

Solution for 5x^2+51x+108=0 equation:

Simplifying
5x2 + 51x + 108 = 0

Reorder the terms:
108 + 51x + 5x2 = 0

Solving
108 + 51x + 5x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(36 + 5x)(3 + x) = 0

Subproblem 1
Set the factor '(36 + 5x)' equal to zero and attempt to solve:

Simplifying
36 + 5x = 0

Solving
36 + 5x = 0

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

Add '-36' to each side of the equation.
36 + -36 + 5x = 0 + -36

Combine like terms: 36 + -36 = 0
0 + 5x = 0 + -36
5x = 0 + -36

Combine like terms: 0 + -36 = -36
5x = -36

Divide each side by '5'.
x = -7.2

Simplifying
x = -7.2
Subproblem 2
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

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

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

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

Simplifying
x = -3
Solution
x = {-7.2, -3}