2(x-4)+x^2=4-(x+2)(3-x)

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Solution for 2(x-4)+x^2=4-(x+2)(3-x) equation: 


Simplifying
2(x + -4) + x2 = 4 + -1(x + 2)(3 + -1x)

Reorder the terms:
2(-4 + x) + x2 = 4 + -1(x + 2)(3 + -1x)
(-4 * 2 + x * 2) + x2 = 4 + -1(x + 2)(3 + -1x)
(-8 + 2x) + x2 = 4 + -1(x + 2)(3 + -1x)

Reorder the terms:
-8 + 2x + x2 = 4 + -1(2 + x)(3 + -1x)

Multiply (2 + x) * (3 + -1x)
-8 + 2x + x2 = 4 + -1(2(3 + -1x) + x(3 + -1x))
-8 + 2x + x2 = 4 + -1((3 * 2 + -1x * 2) + x(3 + -1x))
-8 + 2x + x2 = 4 + -1((6 + -2x) + x(3 + -1x))
-8 + 2x + x2 = 4 + -1(6 + -2x + (3 * x + -1x * x))
-8 + 2x + x2 = 4 + -1(6 + -2x + (3x + -1x2))

Combine like terms: -2x + 3x = 1x
-8 + 2x + x2 = 4 + -1(6 + 1x + -1x2)
-8 + 2x + x2 = 4 + (6 * -1 + 1x * -1 + -1x2 * -1)
-8 + 2x + x2 = 4 + (-6 + -1x + 1x2)

Combine like terms: 4 + -6 = -2
-8 + 2x + x2 = -2 + -1x + 1x2

Solving
-8 + 2x + x2 = -2 + -1x + 1x2

Solving for variable 'x'.

Reorder the terms:
-8 + 2 + 2x + x + x2 + -1x2 = -2 + -1x + 1x2 + 2 + x + -1x2

Combine like terms: -8 + 2 = -6
-6 + 2x + x + x2 + -1x2 = -2 + -1x + 1x2 + 2 + x + -1x2

Combine like terms: 2x + x = 3x
-6 + 3x + x2 + -1x2 = -2 + -1x + 1x2 + 2 + x + -1x2

Combine like terms: x2 + -1x2 = 0
-6 + 3x + 0 = -2 + -1x + 1x2 + 2 + x + -1x2
-6 + 3x = -2 + -1x + 1x2 + 2 + x + -1x2

Reorder the terms:
-6 + 3x = -2 + 2 + -1x + x + 1x2 + -1x2

Combine like terms: -2 + 2 = 0
-6 + 3x = 0 + -1x + x + 1x2 + -1x2
-6 + 3x = -1x + x + 1x2 + -1x2

Combine like terms: -1x + x = 0
-6 + 3x = 0 + 1x2 + -1x2
-6 + 3x = 1x2 + -1x2

Combine like terms: 1x2 + -1x2 = 0
-6 + 3x = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-2 + x) = 0

Ignore the factor 3.

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
Solution
x = {2}

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