4x^2+20x+16=216

Solution for 4x^2+20x+16=216 equation:

Simplifying
4x2 + 20x + 16 = 216

Reorder the terms:
16 + 20x + 4x2 = 216

Solving
16 + 20x + 4x2 = 216

Solving for variable 'x'.

Reorder the terms:
16 + -216 + 20x + 4x2 = 216 + -216

Combine like terms: 16 + -216 = -200
-200 + 20x + 4x2 = 216 + -216

Combine like terms: 216 + -216 = 0
-200 + 20x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-50 + 5x + x2) = 0

Factor a trinomial.
4((-10 + -1x)(5 + -1x)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-10 + -1x)' equal to zero and attempt to solve:

Simplifying
-10 + -1x = 0

Solving
-10 + -1x = 0

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

Add '10' to each side of the equation.
-10 + 10 + -1x = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -1x = 0 + 10
-1x = 0 + 10

Combine like terms: 0 + 10 = 10
-1x = 10

Divide each side by '-1'.
x = -10

Simplifying
x = -10
Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-10, 5}