(x+6)(x+6)+(x+3)(x+3)=(x+9)(x+9)

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Solution for (x+6)(x+6)+(x+3)(x+3)=(x+9)(x+9) equation: 


Simplifying
(x + 6)(x + 6) + (x + 3)(x + 3) = (x + 9)(x + 9)

Reorder the terms:
(6 + x)(x + 6) + (x + 3)(x + 3) = (x + 9)(x + 9)

Reorder the terms:
(6 + x)(6 + x) + (x + 3)(x + 3) = (x + 9)(x + 9)

Multiply (6 + x) * (6 + x)
(6(6 + x) + x(6 + x)) + (x + 3)(x + 3) = (x + 9)(x + 9)
((6 * 6 + x * 6) + x(6 + x)) + (x + 3)(x + 3) = (x + 9)(x + 9)
((36 + 6x) + x(6 + x)) + (x + 3)(x + 3) = (x + 9)(x + 9)
(36 + 6x + (6 * x + x * x)) + (x + 3)(x + 3) = (x + 9)(x + 9)
(36 + 6x + (6x + x2)) + (x + 3)(x + 3) = (x + 9)(x + 9)

Combine like terms: 6x + 6x = 12x
(36 + 12x + x2) + (x + 3)(x + 3) = (x + 9)(x + 9)

Reorder the terms:
36 + 12x + x2 + (3 + x)(x + 3) = (x + 9)(x + 9)

Reorder the terms:
36 + 12x + x2 + (3 + x)(3 + x) = (x + 9)(x + 9)

Multiply (3 + x) * (3 + x)
36 + 12x + x2 + (3(3 + x) + x(3 + x)) = (x + 9)(x + 9)
36 + 12x + x2 + ((3 * 3 + x * 3) + x(3 + x)) = (x + 9)(x + 9)
36 + 12x + x2 + ((9 + 3x) + x(3 + x)) = (x + 9)(x + 9)
36 + 12x + x2 + (9 + 3x + (3 * x + x * x)) = (x + 9)(x + 9)
36 + 12x + x2 + (9 + 3x + (3x + x2)) = (x + 9)(x + 9)

Combine like terms: 3x + 3x = 6x
36 + 12x + x2 + (9 + 6x + x2) = (x + 9)(x + 9)

Reorder the terms:
36 + 9 + 12x + 6x + x2 + x2 = (x + 9)(x + 9)

Combine like terms: 36 + 9 = 45
45 + 12x + 6x + x2 + x2 = (x + 9)(x + 9)

Combine like terms: 12x + 6x = 18x
45 + 18x + x2 + x2 = (x + 9)(x + 9)

Combine like terms: x2 + x2 = 2x2
45 + 18x + 2x2 = (x + 9)(x + 9)

Reorder the terms:
45 + 18x + 2x2 = (9 + x)(x + 9)

Reorder the terms:
45 + 18x + 2x2 = (9 + x)(9 + x)

Multiply (9 + x) * (9 + x)
45 + 18x + 2x2 = (9(9 + x) + x(9 + x))
45 + 18x + 2x2 = ((9 * 9 + x * 9) + x(9 + x))
45 + 18x + 2x2 = ((81 + 9x) + x(9 + x))
45 + 18x + 2x2 = (81 + 9x + (9 * x + x * x))
45 + 18x + 2x2 = (81 + 9x + (9x + x2))

Combine like terms: 9x + 9x = 18x
45 + 18x + 2x2 = (81 + 18x + x2)

Add '-18x' to each side of the equation.
45 + 18x + -18x + 2x2 = 81 + 18x + -18x + x2

Combine like terms: 18x + -18x = 0
45 + 0 + 2x2 = 81 + 18x + -18x + x2
45 + 2x2 = 81 + 18x + -18x + x2

Combine like terms: 18x + -18x = 0
45 + 2x2 = 81 + 0 + x2
45 + 2x2 = 81 + x2

Solving
45 + 2x2 = 81 + x2

Solving for variable 'x'.

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

Add '-1x2' to each side of the equation.
45 + 2x2 + -1x2 = 81 + x2 + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
45 + 1x2 = 81 + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
45 + 1x2 = 81 + 0
45 + 1x2 = 81

Add '-45' to each side of the equation.
45 + -45 + 1x2 = 81 + -45

Combine like terms: 45 + -45 = 0
0 + 1x2 = 81 + -45
1x2 = 81 + -45

Combine like terms: 81 + -45 = 36
1x2 = 36

Divide each side by '1'.
x2 = 36

Simplifying
x2 = 36

Take the square root of each side:
x = {-6, 6}

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