x*x+(x+3)(x+3)=(x+6)(x+6)

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Solution for x*x+(x+3)(x+3)=(x+6)(x+6) equation: 


Simplifying
x * x + (x + 3)(x + 3) = (x + 6)(x + 6)

Multiply x * x
x2 + (x + 3)(x + 3) = (x + 6)(x + 6)

Reorder the terms:
x2 + (3 + x)(x + 3) = (x + 6)(x + 6)

Reorder the terms:
x2 + (3 + x)(3 + x) = (x + 6)(x + 6)

Multiply (3 + x) * (3 + x)
x2 + (3(3 + x) + x(3 + x)) = (x + 6)(x + 6)
x2 + ((3 * 3 + x * 3) + x(3 + x)) = (x + 6)(x + 6)
x2 + ((9 + 3x) + x(3 + x)) = (x + 6)(x + 6)
x2 + (9 + 3x + (3 * x + x * x)) = (x + 6)(x + 6)
x2 + (9 + 3x + (3x + x2)) = (x + 6)(x + 6)

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

Reorder the terms:
9 + 6x + x2 + x2 = (x + 6)(x + 6)

Combine like terms: x2 + x2 = 2x2
9 + 6x + 2x2 = (x + 6)(x + 6)

Reorder the terms:
9 + 6x + 2x2 = (6 + x)(x + 6)

Reorder the terms:
9 + 6x + 2x2 = (6 + x)(6 + x)

Multiply (6 + x) * (6 + x)
9 + 6x + 2x2 = (6(6 + x) + x(6 + x))
9 + 6x + 2x2 = ((6 * 6 + x * 6) + x(6 + x))
9 + 6x + 2x2 = ((36 + 6x) + x(6 + x))
9 + 6x + 2x2 = (36 + 6x + (6 * x + x * x))
9 + 6x + 2x2 = (36 + 6x + (6x + x2))

Combine like terms: 6x + 6x = 12x
9 + 6x + 2x2 = (36 + 12x + x2)

Solving
9 + 6x + 2x2 = 36 + 12x + x2

Solving for variable 'x'.

Reorder the terms:
9 + -36 + 6x + -12x + 2x2 + -1x2 = 36 + 12x + x2 + -36 + -12x + -1x2

Combine like terms: 9 + -36 = -27
-27 + 6x + -12x + 2x2 + -1x2 = 36 + 12x + x2 + -36 + -12x + -1x2

Combine like terms: 6x + -12x = -6x
-27 + -6x + 2x2 + -1x2 = 36 + 12x + x2 + -36 + -12x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
-27 + -6x + 1x2 = 36 + 12x + x2 + -36 + -12x + -1x2

Reorder the terms:
-27 + -6x + 1x2 = 36 + -36 + 12x + -12x + x2 + -1x2

Combine like terms: 36 + -36 = 0
-27 + -6x + 1x2 = 0 + 12x + -12x + x2 + -1x2
-27 + -6x + 1x2 = 12x + -12x + x2 + -1x2

Combine like terms: 12x + -12x = 0
-27 + -6x + 1x2 = 0 + x2 + -1x2
-27 + -6x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-27 + -6x + 1x2 = 0

Factor a trinomial.
(-3 + -1x)(9 + -1x) = 0


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

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 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 + -1x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1x = 0 + 3
-1x = 0 + 3

Combine like terms: 0 + 3 = 3
-1x = 3

Divide each side by '-1'.
x = -3

Simplifying
x = -3

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 = {-3, 9}

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