7x^2+55x+108=0

Solution for 7x^2+55x+108=0 equation:

Simplifying
7x2 + 55x + 108 = 0

Reorder the terms:
108 + 55x + 7x2 = 0

Solving
108 + 55x + 7x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(4 + x)(27 + 7x) = 0

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

Simplifying
4 + x = 0

Solving
4 + x = 0

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

Add '-4' to each side of the equation.
4 + -4 + x = 0 + -4

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

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

Simplifying
x = -4
Subproblem 2
Set the factor '(27 + 7x)' equal to zero and attempt to solve:

Simplifying
27 + 7x = 0

Solving
27 + 7x = 0

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

Add '-27' to each side of the equation.
27 + -27 + 7x = 0 + -27

Combine like terms: 27 + -27 = 0
0 + 7x = 0 + -27
7x = 0 + -27

Combine like terms: 0 + -27 = -27
7x = -27

Divide each side by '7'.
x = -3.857142857

Simplifying
x = -3.857142857
Solution
x = {-4, -3.857142857}