(x-2)(x-2)-4(x-2)-21=0

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Solution for (x-2)(x-2)-4(x-2)-21=0 equation: 


Simplifying
(x + -2)(x + -2) + -4(x + -2) + -21 = 0

Reorder the terms:
(-2 + x)(x + -2) + -4(x + -2) + -21 = 0

Reorder the terms:
(-2 + x)(-2 + x) + -4(x + -2) + -21 = 0

Multiply (-2 + x) * (-2 + x)
(-2(-2 + x) + x(-2 + x)) + -4(x + -2) + -21 = 0
((-2 * -2 + x * -2) + x(-2 + x)) + -4(x + -2) + -21 = 0
((4 + -2x) + x(-2 + x)) + -4(x + -2) + -21 = 0
(4 + -2x + (-2 * x + x * x)) + -4(x + -2) + -21 = 0
(4 + -2x + (-2x + x2)) + -4(x + -2) + -21 = 0

Combine like terms: -2x + -2x = -4x
(4 + -4x + x2) + -4(x + -2) + -21 = 0

Reorder the terms:
4 + -4x + x2 + -4(-2 + x) + -21 = 0
4 + -4x + x2 + (-2 * -4 + x * -4) + -21 = 0
4 + -4x + x2 + (8 + -4x) + -21 = 0

Reorder the terms:
4 + 8 + -21 + -4x + -4x + x2 = 0

Combine like terms: 4 + 8 = 12
12 + -21 + -4x + -4x + x2 = 0

Combine like terms: 12 + -21 = -9
-9 + -4x + -4x + x2 = 0

Combine like terms: -4x + -4x = -8x
-9 + -8x + x2 = 0

Solving
-9 + -8x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-1 + -1x)(9 + -1x) = 0


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

Simplifying
-1 + -1x = 0

Solving
-1 + -1x = 0

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

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

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

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

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

Simplifying
x = -1

Subproblem 2
Set the factor '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

Solving
9 + -1x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1x = 0 + -9

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

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

Divide each side by '-1'.
x = 9

Simplifying
x = 9
Solution
x = {-1, 9}

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