(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 = 2x
(-15 + 2x + x2) + -1(x + -6)(x + 6) = 0

Reorder the terms:
-15 + 2x + x2 + -1(-6 + x)(x + 6) = 0

Reorder the terms:
-15 + 2x + x2 + -1(-6 + x)(6 + x) = 0

Multiply (-6 + x) * (6 + x)
-15 + 2x + x2 + -1(-6(6 + x) + x(6 + x)) = 0
-15 + 2x + x2 + -1((6 * -6 + x * -6) + x(6 + x)) = 0
-15 + 2x + x2 + -1((-36 + -6x) + x(6 + x)) = 0
-15 + 2x + x2 + -1(-36 + -6x + (6 * x + x * x)) = 0
-15 + 2x + x2 + -1(-36 + -6x + (6x + x2)) = 0

Combine like terms: -6x + 6x = 0
-15 + 2x + x2 + -1(-36 + 0 + x2) = 0
-15 + 2x + x2 + -1(-36 + x2) = 0
-15 + 2x + x2 + (-36 * -1 + x2 * -1) = 0
-15 + 2x + x2 + (36 + -1x2) = 0

Reorder the terms:
-15 + 36 + 2x + x2 + -1x2 = 0

Combine like terms: -15 + 36 = 21
21 + 2x + x2 + -1x2 = 0

Combine like terms: x2 + -1x2 = 0
21 + 2x + 0 = 0
21 + 2x = 0

Solving
21 + 2x = 0

Solving for variable 'x'.

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

Add '-21' to each side of the equation.
21 + -21 + 2x = 0 + -21

Combine like terms: 21 + -21 = 0
0 + 2x = 0 + -21
2x = 0 + -21

Combine like terms: 0 + -21 = -21
2x = -21

Divide each side by '2'.
x = -10.5

Simplifying
x = -10.5

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