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

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


Simplifying
(x + -4)(x + -4) = x + 2

Reorder the terms:
(-4 + x)(x + -4) = x + 2

Reorder the terms:
(-4 + x)(-4 + x) = x + 2

Multiply (-4 + x) * (-4 + x)
(-4(-4 + x) + x(-4 + x)) = x + 2
((-4 * -4 + x * -4) + x(-4 + x)) = x + 2
((16 + -4x) + x(-4 + x)) = x + 2
(16 + -4x + (-4 * x + x * x)) = x + 2
(16 + -4x + (-4x + x2)) = x + 2

Combine like terms: -4x + -4x = -8x
(16 + -8x + x2) = x + 2

Reorder the terms:
16 + -8x + x2 = 2 + x

Solving
16 + -8x + x2 = 2 + x

Solving for variable 'x'.

Reorder the terms:
16 + -2 + -8x + -1x + x2 = 2 + x + -2 + -1x

Combine like terms: 16 + -2 = 14
14 + -8x + -1x + x2 = 2 + x + -2 + -1x

Combine like terms: -8x + -1x = -9x
14 + -9x + x2 = 2 + x + -2 + -1x

Reorder the terms:
14 + -9x + x2 = 2 + -2 + x + -1x

Combine like terms: 2 + -2 = 0
14 + -9x + x2 = 0 + x + -1x
14 + -9x + x2 = x + -1x

Combine like terms: x + -1x = 0
14 + -9x + x2 = 0

Factor a trinomial.
(2 + -1x)(7 + -1x) = 0


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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 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 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2

Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {2, 7}

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