3x^2+39x-90=0

Solution for 3x^2+39x-90=0 equation:

Simplifying
3x2 + 39x + -90 = 0

Reorder the terms:
-90 + 39x + 3x2 = 0

Solving
-90 + 39x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-30 + 13x + x2) = 0

Factor a trinomial.
3((-15 + -1x)(2 + -1x)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-15 + -1x)' equal to zero and attempt to solve:

Simplifying
-15 + -1x = 0

Solving
-15 + -1x = 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 + -1x = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -1x = 0 + 15
-1x = 0 + 15

Combine like terms: 0 + 15 = 15
-1x = 15

Divide each side by '-1'.
x = -15

Simplifying
x = -15
Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-15, 2}