(x-3)(x+4)+8=x

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Solution for (x-3)(x+4)+8=x equation: 


Simplifying
(x + -3)(x + 4) + 8 = x

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

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

Multiply (-3 + x) * (4 + x)
(-3(4 + x) + x(4 + x)) + 8 = x
((4 * -3 + x * -3) + x(4 + x)) + 8 = x
((-12 + -3x) + x(4 + x)) + 8 = x
(-12 + -3x + (4 * x + x * x)) + 8 = x
(-12 + -3x + (4x + x2)) + 8 = x

Combine like terms: -3x + 4x = 1x
(-12 + 1x + x2) + 8 = x

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

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

Solving
-4 + 1x + x2 = x

Solving for variable 'x'.

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

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

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

Factor a difference between two squares.
(2 + x)(-2 + x) = 0


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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