4x^2+24x+36=100

Solution for 4x^2+24x+36=100 equation:

Simplifying
4x2 + 24x + 36 = 100

Reorder the terms:
36 + 24x + 4x2 = 100

Solving
36 + 24x + 4x2 = 100

Solving for variable 'x'.

Reorder the terms:
36 + -100 + 24x + 4x2 = 100 + -100

Combine like terms: 36 + -100 = -64
-64 + 24x + 4x2 = 100 + -100

Combine like terms: 100 + -100 = 0
-64 + 24x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-16 + 6x + x2) = 0

Factor a trinomial.
4((-8 + -1x)(2 + -1x)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-8 + -1x)' equal to zero and attempt to solve:

Simplifying
-8 + -1x = 0

Solving
-8 + -1x = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1x = 0 + 8
-1x = 0 + 8

Combine like terms: 0 + 8 = 8
-1x = 8

Divide each side by '-1'.
x = -8

Simplifying
x = -8
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 = {-8, 2}