10=2(x+3)(x+3)+2

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Solution for 10=2(x+3)(x+3)+2 equation: 


Simplifying
10 = 2(x + 3)(x + 3) + 2

Reorder the terms:
10 = 2(3 + x)(x + 3) + 2

Reorder the terms:
10 = 2(3 + x)(3 + x) + 2

Multiply (3 + x) * (3 + x)
10 = 2(3(3 + x) + x(3 + x)) + 2
10 = 2((3 * 3 + x * 3) + x(3 + x)) + 2
10 = 2((9 + 3x) + x(3 + x)) + 2
10 = 2(9 + 3x + (3 * x + x * x)) + 2
10 = 2(9 + 3x + (3x + x2)) + 2

Combine like terms: 3x + 3x = 6x
10 = 2(9 + 6x + x2) + 2
10 = (9 * 2 + 6x * 2 + x2 * 2) + 2
10 = (18 + 12x + 2x2) + 2

Reorder the terms:
10 = 18 + 2 + 12x + 2x2

Combine like terms: 18 + 2 = 20
10 = 20 + 12x + 2x2

Solving
10 = 20 + 12x + 2x2

Solving for variable 'x'.

Combine like terms: 10 + -20 = -10
-10 + -12x + -2x2 = 20 + 12x + 2x2 + -20 + -12x + -2x2

Reorder the terms:
-10 + -12x + -2x2 = 20 + -20 + 12x + -12x + 2x2 + -2x2

Combine like terms: 20 + -20 = 0
-10 + -12x + -2x2 = 0 + 12x + -12x + 2x2 + -2x2
-10 + -12x + -2x2 = 12x + -12x + 2x2 + -2x2

Combine like terms: 12x + -12x = 0
-10 + -12x + -2x2 = 0 + 2x2 + -2x2
-10 + -12x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-10 + -12x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '-2'.
-2(5 + 6x + x2) = 0

Factor a trinomial.
-2((5 + x)(1 + x)) = 0

Ignore the factor -2.

Subproblem 1
Set the factor '(5 + x)' equal to zero and attempt to solve:

Simplifying
5 + x = 0

Solving
5 + x = 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 + x = 0 + -5

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

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

Simplifying
x = -5

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

Simplifying
1 + x = 0

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

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

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

Simplifying
x = -1
Solution
x = {-5, -1}

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