4x^2+84x+432=1080

Solution for 4x^2+84x+432=1080 equation:

Simplifying
4x2 + 84x + 432 = 1080

Reorder the terms:
432 + 84x + 4x2 = 1080

Solving
432 + 84x + 4x2 = 1080

Solving for variable 'x'.

Reorder the terms:
432 + -1080 + 84x + 4x2 = 1080 + -1080

Combine like terms: 432 + -1080 = -648
-648 + 84x + 4x2 = 1080 + -1080

Combine like terms: 1080 + -1080 = 0
-648 + 84x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-162 + 21x + x2) = 0

Factor a trinomial.
4((-27 + -1x)(6 + -1x)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-27 + -1x)' equal to zero and attempt to solve:

Simplifying
-27 + -1x = 0

Solving
-27 + -1x = 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 + -1x = 0 + 27

Combine like terms: -27 + 27 = 0
0 + -1x = 0 + 27
-1x = 0 + 27

Combine like terms: 0 + 27 = 27
-1x = 27

Divide each side by '-1'.
x = -27

Simplifying
x = -27
Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 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 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {-27, 6}