x^2+20x+100=-x^2-16x+388

Solution for x^2+20x+100=-x^2-16x+388 equation:

Simplifying
x2 + 20x + 100 = -1x2 + -16x + 388

Reorder the terms:
100 + 20x + x2 = -1x2 + -16x + 388

Reorder the terms:
100 + 20x + x2 = 388 + -16x + -1x2

Solving
100 + 20x + x2 = 388 + -16x + -1x2

Solving for variable 'x'.

Reorder the terms:
100 + -388 + 20x + 16x + x2 + x2 = 388 + -16x + -1x2 + -388 + 16x + x2

Combine like terms: 100 + -388 = -288
-288 + 20x + 16x + x2 + x2 = 388 + -16x + -1x2 + -388 + 16x + x2

Combine like terms: 20x + 16x = 36x
-288 + 36x + x2 + x2 = 388 + -16x + -1x2 + -388 + 16x + x2

Combine like terms: x2 + x2 = 2x2
-288 + 36x + 2x2 = 388 + -16x + -1x2 + -388 + 16x + x2

Reorder the terms:
-288 + 36x + 2x2 = 388 + -388 + -16x + 16x + -1x2 + x2

Combine like terms: 388 + -388 = 0
-288 + 36x + 2x2 = 0 + -16x + 16x + -1x2 + x2
-288 + 36x + 2x2 = -16x + 16x + -1x2 + x2

Combine like terms: -16x + 16x = 0
-288 + 36x + 2x2 = 0 + -1x2 + x2
-288 + 36x + 2x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-288 + 36x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-144 + 18x + x2) = 0

Factor a trinomial.
2((-24 + -1x)(6 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-24 + -1x)' equal to zero and attempt to solve:

Simplifying
-24 + -1x = 0

Solving
-24 + -1x = 0

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

Add '24' to each side of the equation.
-24 + 24 + -1x = 0 + 24

Combine like terms: -24 + 24 = 0
0 + -1x = 0 + 24
-1x = 0 + 24

Combine like terms: 0 + 24 = 24
-1x = 24

Divide each side by '-1'.
x = -24

Simplifying
x = -24
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 = {-24, 6}