4x^2+39x+90=0

Solution for 4x^2+39x+90=0 equation:

Simplifying
4x2 + 39x + 90 = 0

Reorder the terms:
90 + 39x + 4x2 = 0

Solving
90 + 39x + 4x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(6 + x)(15 + 4x) = 0

Subproblem 1
Set the factor '(6 + x)' equal to zero and attempt to solve:

Simplifying
6 + x = 0

Solving
6 + x = 0

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

Add '-6' to each side of the equation.
6 + -6 + x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + x = 0 + -6
x = 0 + -6

Combine like terms: 0 + -6 = -6
x = -6

Simplifying
x = -6
Subproblem 2
Set the factor '(15 + 4x)' equal to zero and attempt to solve:

Simplifying
15 + 4x = 0

Solving
15 + 4x = 0

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

Add '-15' to each side of the equation.
15 + -15 + 4x = 0 + -15

Combine like terms: 15 + -15 = 0
0 + 4x = 0 + -15
4x = 0 + -15

Combine like terms: 0 + -15 = -15
4x = -15

Divide each side by '4'.
x = -3.75

Simplifying
x = -3.75
Solution
x = {-6, -3.75}