6X^2+48X+90=0

Solution for 6X^2+48X+90=0 equation:

Simplifying
6X2 + 48X + 90 = 0

Reorder the terms:
90 + 48X + 6X2 = 0

Solving
90 + 48X + 6X2 = 0

Solving for variable 'X'.

Factor out the Greatest Common Factor (GCF), '6'.
6(15 + 8X + X2) = 0

Factor a trinomial.
6((5 + X)(3 + X)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(5 + X)' equal to zero and attempt to solve:

Simplifying
5 + X = 0

Solving
5 + X = 0

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

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

Combine like terms: 5 + -5 = 0
0 + X = 0 + -5
X = 0 + -5

Combine like terms: 0 + -5 = -5
X = -5

Simplifying
X = -5
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 = {-5, -3}