8-x^2=4(x+2)+4

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Solution for 8-x^2=4(x+2)+4 equation: 


Simplifying
8 + -1x2 = 4(x + 2) + 4

Reorder the terms:
8 + -1x2 = 4(2 + x) + 4
8 + -1x2 = (2 * 4 + x * 4) + 4
8 + -1x2 = (8 + 4x) + 4

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

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

Solving
8 + -1x2 = 12 + 4x

Solving for variable 'x'.

Reorder the terms:
8 + -12 + -4x + -1x2 = 12 + 4x + -12 + -4x

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

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

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

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

Factor out the Greatest Common Factor (GCF), '-1'.
-1(4 + 4x + x2) = 0

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

Ignore the factor -1.

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

Simplifying
2 + x = 0

Solving
2 + x = 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 + x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

Simplifying
x = -2

Subproblem 2
Set the factor '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 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 + x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

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

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