4(x^2)+24x-405=0

Solution for 4(x^2)+24x-405=0 equation:

Simplifying
4(x2) + 24x + -405 = 0

Reorder the terms:
-405 + 24x + 4x2 = 0

Solving
-405 + 24x + 4x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-27 + -2x)(15 + -2x) = 0

Subproblem 1
Set the factor '(-27 + -2x)' equal to zero and attempt to solve:

Simplifying
-27 + -2x = 0

Solving
-27 + -2x = 0

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

Add '27' to each side of the equation.
-27 + 27 + -2x = 0 + 27

Combine like terms: -27 + 27 = 0
0 + -2x = 0 + 27
-2x = 0 + 27

Combine like terms: 0 + 27 = 27
-2x = 27

Divide each side by '-2'.
x = -13.5

Simplifying
x = -13.5
Subproblem 2
Set the factor '(15 + -2x)' equal to zero and attempt to solve:

Simplifying
15 + -2x = 0

Solving
15 + -2x = 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 + -2x = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -2x = 0 + -15
-2x = 0 + -15

Combine like terms: 0 + -15 = -15
-2x = -15

Divide each side by '-2'.
x = 7.5

Simplifying
x = 7.5
Solution
x = {-13.5, 7.5}