(x-2)(x+2)-7(x-1)=21

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Solution for (x-2)(x+2)-7(x-1)=21 equation: 


Simplifying
(x + -2)(x + 2) + -7(x + -1) = 21

Reorder the terms:
(-2 + x)(x + 2) + -7(x + -1) = 21

Reorder the terms:
(-2 + x)(2 + x) + -7(x + -1) = 21

Multiply (-2 + x) * (2 + x)
(-2(2 + x) + x(2 + x)) + -7(x + -1) = 21
((2 * -2 + x * -2) + x(2 + x)) + -7(x + -1) = 21
((-4 + -2x) + x(2 + x)) + -7(x + -1) = 21
(-4 + -2x + (2 * x + x * x)) + -7(x + -1) = 21
(-4 + -2x + (2x + x2)) + -7(x + -1) = 21

Combine like terms: -2x + 2x = 0
(-4 + 0 + x2) + -7(x + -1) = 21
(-4 + x2) + -7(x + -1) = 21

Reorder the terms:
-4 + x2 + -7(-1 + x) = 21
-4 + x2 + (-1 * -7 + x * -7) = 21
-4 + x2 + (7 + -7x) = 21

Reorder the terms:
-4 + 7 + -7x + x2 = 21

Combine like terms: -4 + 7 = 3
3 + -7x + x2 = 21

Solving
3 + -7x + x2 = 21

Solving for variable 'x'.

Reorder the terms:
3 + -21 + -7x + x2 = 21 + -21

Combine like terms: 3 + -21 = -18
-18 + -7x + x2 = 21 + -21

Combine like terms: 21 + -21 = 0
-18 + -7x + x2 = 0

Factor a trinomial.
(-2 + -1x)(9 + -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 '(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 = {-2, 9}

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