11(12+x)+11(12-x)=6.0(12+x)(12-x)

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Solution for 11(12+x)+11(12-x)=6.0(12+x)(12-x) equation:


Simplifying
11(12 + x) + 11(12 + -1x) = 6.0(12 + x)(12 + -1x)
(12 * 11 + x * 11) + 11(12 + -1x) = 6.0(12 + x)(12 + -1x)
(132 + 11x) + 11(12 + -1x) = 6.0(12 + x)(12 + -1x)
132 + 11x + (12 * 11 + -1x * 11) = 6.0(12 + x)(12 + -1x)
132 + 11x + (132 + -11x) = 6.0(12 + x)(12 + -1x)

Reorder the terms:
132 + 132 + 11x + -11x = 6.0(12 + x)(12 + -1x)

Combine like terms: 132 + 132 = 264
264 + 11x + -11x = 6.0(12 + x)(12 + -1x)

Combine like terms: 11x + -11x = 0
264 + 0 = 6.0(12 + x)(12 + -1x)
264 = 6.0(12 + x)(12 + -1x)

Multiply (12 + x) * (12 + -1x)
264 = 6.0(12(12 + -1x) + x(12 + -1x))
264 = 6.0((12 * 12 + -1x * 12) + x(12 + -1x))
264 = 6.0((144 + -12x) + x(12 + -1x))
264 = 6.0(144 + -12x + (12 * x + -1x * x))
264 = 6.0(144 + -12x + (12x + -1x2))

Combine like terms: -12x + 12x = 0
264 = 6.0(144 + 0 + -1x2)
264 = 6.0(144 + -1x2)
264 = (144 * 6.0 + -1x2 * 6.0)
264 = (864 + -6x2)

Solving
264 = 864 + -6x2

Solving for variable 'x'.

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

Add '6x2' to each side of the equation.
264 + 6x2 = 864 + -6x2 + 6x2

Combine like terms: -6x2 + 6x2 = 0
264 + 6x2 = 864 + 0
264 + 6x2 = 864

Add '-264' to each side of the equation.
264 + -264 + 6x2 = 864 + -264

Combine like terms: 264 + -264 = 0
0 + 6x2 = 864 + -264
6x2 = 864 + -264

Combine like terms: 864 + -264 = 600
6x2 = 600

Divide each side by '6'.
x2 = 100

Simplifying
x2 = 100

Take the square root of each side:
x = {-10, 10}

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