(x-10)(x-5)=(x+9)(x+9)

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Solution for (x-10)(x-5)=(x+9)(x+9) equation: 


Simplifying
(x + -10)(x + -5) = (x + 9)(x + 9)

Reorder the terms:
(-10 + x)(x + -5) = (x + 9)(x + 9)

Reorder the terms:
(-10 + x)(-5 + x) = (x + 9)(x + 9)

Multiply (-10 + x) * (-5 + x)
(-10(-5 + x) + x(-5 + x)) = (x + 9)(x + 9)
((-5 * -10 + x * -10) + x(-5 + x)) = (x + 9)(x + 9)
((50 + -10x) + x(-5 + x)) = (x + 9)(x + 9)
(50 + -10x + (-5 * x + x * x)) = (x + 9)(x + 9)
(50 + -10x + (-5x + x2)) = (x + 9)(x + 9)

Combine like terms: -10x + -5x = -15x
(50 + -15x + x2) = (x + 9)(x + 9)

Reorder the terms:
50 + -15x + x2 = (9 + x)(x + 9)

Reorder the terms:
50 + -15x + x2 = (9 + x)(9 + x)

Multiply (9 + x) * (9 + x)
50 + -15x + x2 = (9(9 + x) + x(9 + x))
50 + -15x + x2 = ((9 * 9 + x * 9) + x(9 + x))
50 + -15x + x2 = ((81 + 9x) + x(9 + x))
50 + -15x + x2 = (81 + 9x + (9 * x + x * x))
50 + -15x + x2 = (81 + 9x + (9x + x2))

Combine like terms: 9x + 9x = 18x
50 + -15x + x2 = (81 + 18x + x2)

Add '-1x2' to each side of the equation.
50 + -15x + x2 + -1x2 = 81 + 18x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
50 + -15x + 0 = 81 + 18x + x2 + -1x2
50 + -15x = 81 + 18x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
50 + -15x = 81 + 18x + 0
50 + -15x = 81 + 18x

Solving
50 + -15x = 81 + 18x

Solving for variable 'x'.

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

Add '-18x' to each side of the equation.
50 + -15x + -18x = 81 + 18x + -18x

Combine like terms: -15x + -18x = -33x
50 + -33x = 81 + 18x + -18x

Combine like terms: 18x + -18x = 0
50 + -33x = 81 + 0
50 + -33x = 81

Add '-50' to each side of the equation.
50 + -50 + -33x = 81 + -50

Combine like terms: 50 + -50 = 0
0 + -33x = 81 + -50
-33x = 81 + -50

Combine like terms: 81 + -50 = 31
-33x = 31

Divide each side by '-33'.
x = -0.9393939394

Simplifying
x = -0.9393939394

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