(x+3)=(x+3)(x+3)

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


Simplifying
(x + 3) = (x + 3)(x + 3)

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

Remove parenthesis around (3 + x)
3 + x = (x + 3)(x + 3)

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

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

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

Combine like terms: 3x + 3x = 6x
3 + x = (9 + 6x + x2)

Solving
3 + x = 9 + 6x + x2

Solving for variable 'x'.

Reorder the terms:
3 + -9 + x + -6x + -1x2 = 9 + 6x + x2 + -9 + -6x + -1x2

Combine like terms: 3 + -9 = -6
-6 + x + -6x + -1x2 = 9 + 6x + x2 + -9 + -6x + -1x2

Combine like terms: x + -6x = -5x
-6 + -5x + -1x2 = 9 + 6x + x2 + -9 + -6x + -1x2

Reorder the terms:
-6 + -5x + -1x2 = 9 + -9 + 6x + -6x + x2 + -1x2

Combine like terms: 9 + -9 = 0
-6 + -5x + -1x2 = 0 + 6x + -6x + x2 + -1x2
-6 + -5x + -1x2 = 6x + -6x + x2 + -1x2

Combine like terms: 6x + -6x = 0
-6 + -5x + -1x2 = 0 + x2 + -1x2
-6 + -5x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-6 + -5x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(6 + 5x + x2) = 0

Factor a trinomial.
-1((3 + x)(2 + x)) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 0

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

Add '-3' to each side of the equation.
3 + -3 + x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3

Combine like terms: 0 + -3 = -3
x = -3

Simplifying
x = -3

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

Simplifying
2 + x = 0

Solving
2 + x = 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 + x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

Simplifying
x = -2
Solution
x = {-3, -2}

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