(x+3)(x+5)-(x-6)(x+6)=0

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Solution for (x+3)(x+5)-(x-6)(x+6)=0 equation: 


Simplifying
(x + 3)(x + 5) + -1(x + -6)(x + 6) = 0

Reorder the terms:
(3 + x)(x + 5) + -1(x + -6)(x + 6) = 0

Reorder the terms:
(3 + x)(5 + x) + -1(x + -6)(x + 6) = 0

Multiply (3 + x) * (5 + x)
(3(5 + x) + x(5 + x)) + -1(x + -6)(x + 6) = 0
((5 * 3 + x * 3) + x(5 + x)) + -1(x + -6)(x + 6) = 0
((15 + 3x) + x(5 + x)) + -1(x + -6)(x + 6) = 0
(15 + 3x + (5 * x + x * x)) + -1(x + -6)(x + 6) = 0
(15 + 3x + (5x + x2)) + -1(x + -6)(x + 6) = 0

Combine like terms: 3x + 5x = 8x
(15 + 8x + x2) + -1(x + -6)(x + 6) = 0

Reorder the terms:
15 + 8x + x2 + -1(-6 + x)(x + 6) = 0

Reorder the terms:
15 + 8x + x2 + -1(-6 + x)(6 + x) = 0

Multiply (-6 + x) * (6 + x)
15 + 8x + x2 + -1(-6(6 + x) + x(6 + x)) = 0
15 + 8x + x2 + -1((6 * -6 + x * -6) + x(6 + x)) = 0
15 + 8x + x2 + -1((-36 + -6x) + x(6 + x)) = 0
15 + 8x + x2 + -1(-36 + -6x + (6 * x + x * x)) = 0
15 + 8x + x2 + -1(-36 + -6x + (6x + x2)) = 0

Combine like terms: -6x + 6x = 0
15 + 8x + x2 + -1(-36 + 0 + x2) = 0
15 + 8x + x2 + -1(-36 + x2) = 0
15 + 8x + x2 + (-36 * -1 + x2 * -1) = 0
15 + 8x + x2 + (36 + -1x2) = 0

Reorder the terms:
15 + 36 + 8x + x2 + -1x2 = 0

Combine like terms: 15 + 36 = 51
51 + 8x + x2 + -1x2 = 0

Combine like terms: x2 + -1x2 = 0
51 + 8x + 0 = 0
51 + 8x = 0

Solving
51 + 8x = 0

Solving for variable 'x'.

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

Add '-51' to each side of the equation.
51 + -51 + 8x = 0 + -51

Combine like terms: 51 + -51 = 0
0 + 8x = 0 + -51
8x = 0 + -51

Combine like terms: 0 + -51 = -51
8x = -51

Divide each side by '8'.
x = -6.375

Simplifying
x = -6.375

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