(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 = 4x
(4 + 4x + x2) + -7(x + -1) = 21

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

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

Combine like terms: 4 + 7 = 11
11 + 4x + -7x + x2 = 21

Combine like terms: 4x + -7x = -3x
11 + -3x + x2 = 21

Solving
11 + -3x + x2 = 21

Solving for variable 'x'.

Reorder the terms:
11 + -21 + -3x + x2 = 21 + -21

Combine like terms: 11 + -21 = -10
-10 + -3x + x2 = 21 + -21

Combine like terms: 21 + -21 = 0
-10 + -3x + x2 = 0

Factor a trinomial.
(-2 + -1x)(5 + -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 '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-2, 5}

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