x^2+8x+20=100-4x-x^2

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Solution for x^2+8x+20=100-4x-x^2 equation: 


Simplifying
x2 + 8x + 20 = 100 + -4x + -1x2

Reorder the terms:
20 + 8x + x2 = 100 + -4x + -1x2

Solving
20 + 8x + x2 = 100 + -4x + -1x2

Solving for variable 'x'.

Reorder the terms:
20 + -100 + 8x + 4x + x2 + x2 = 100 + -4x + -1x2 + -100 + 4x + x2

Combine like terms: 20 + -100 = -80
-80 + 8x + 4x + x2 + x2 = 100 + -4x + -1x2 + -100 + 4x + x2

Combine like terms: 8x + 4x = 12x
-80 + 12x + x2 + x2 = 100 + -4x + -1x2 + -100 + 4x + x2

Combine like terms: x2 + x2 = 2x2
-80 + 12x + 2x2 = 100 + -4x + -1x2 + -100 + 4x + x2

Reorder the terms:
-80 + 12x + 2x2 = 100 + -100 + -4x + 4x + -1x2 + x2

Combine like terms: 100 + -100 = 0
-80 + 12x + 2x2 = 0 + -4x + 4x + -1x2 + x2
-80 + 12x + 2x2 = -4x + 4x + -1x2 + x2

Combine like terms: -4x + 4x = 0
-80 + 12x + 2x2 = 0 + -1x2 + x2
-80 + 12x + 2x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-80 + 12x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-40 + 6x + x2) = 0

Factor a trinomial.
2((-10 + -1x)(4 + -1x)) = 0

Ignore the factor 2.

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 '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-10, 4}

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