(x+2)(x+2)-3x-6=0

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Solution for (x+2)(x+2)-3x-6=0 equation: 


Simplifying
(x + 2)(x + 2) + -3x + -6 = 0

Reorder the terms:
(2 + x)(x + 2) + -3x + -6 = 0

Reorder the terms:
(2 + x)(2 + x) + -3x + -6 = 0

Multiply (2 + x) * (2 + x)
(2(2 + x) + x(2 + x)) + -3x + -6 = 0
((2 * 2 + x * 2) + x(2 + x)) + -3x + -6 = 0
((4 + 2x) + x(2 + x)) + -3x + -6 = 0
(4 + 2x + (2 * x + x * x)) + -3x + -6 = 0
(4 + 2x + (2x + x2)) + -3x + -6 = 0

Combine like terms: 2x + 2x = 4x
(4 + 4x + x2) + -3x + -6 = 0

Reorder the terms:
4 + -6 + 4x + -3x + x2 = 0

Combine like terms: 4 + -6 = -2
-2 + 4x + -3x + x2 = 0

Combine like terms: 4x + -3x = 1x
-2 + 1x + x2 = 0

Solving
-2 + 1x + x2 = 0

Solving for variable 'x'.

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

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