60x^2+198x+54=0

Solution for 60x^2+198x+54=0 equation:

Simplifying
60x2 + 198x + 54 = 0

Reorder the terms:
54 + 198x + 60x2 = 0

Solving
54 + 198x + 60x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(9 + 33x + 10x2) = 0

Factor a trinomial.
6((3 + x)(3 + 10x)) = 0

Ignore the factor 6.
Subproblem 1
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
Subproblem 2
Set the factor '(3 + 10x)' equal to zero and attempt to solve:

Simplifying
3 + 10x = 0

Solving
3 + 10x = 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 + 10x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 10x = 0 + -3
10x = 0 + -3

Combine like terms: 0 + -3 = -3
10x = -3

Divide each side by '10'.
x = -0.3

Simplifying
x = -0.3
Solution
x = {-3, -0.3}