4x^2+90x-306=0

Solution for 4x^2+90x-306=0 equation:

Simplifying
4x2 + 90x + -306 = 0

Reorder the terms:
-306 + 90x + 4x2 = 0

Solving
-306 + 90x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-153 + 45x + 2x2) = 0

Factor a trinomial.
2((-51 + -2x)(3 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-51 + -2x)' equal to zero and attempt to solve:

Simplifying
-51 + -2x = 0

Solving
-51 + -2x = 0

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

Add '51' to each side of the equation.
-51 + 51 + -2x = 0 + 51

Combine like terms: -51 + 51 = 0
0 + -2x = 0 + 51
-2x = 0 + 51

Combine like terms: 0 + 51 = 51
-2x = 51

Divide each side by '-2'.
x = -25.5

Simplifying
x = -25.5
Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-25.5, 3}