2(x+11)(x-5)=x(x+11)+100

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Solution for 2(x+11)(x-5)=x(x+11)+100 equation: 


Simplifying
2(x + 11)(x + -5) = x(x + 11) + 100

Reorder the terms:
2(11 + x)(x + -5) = x(x + 11) + 100

Reorder the terms:
2(11 + x)(-5 + x) = x(x + 11) + 100

Multiply (11 + x) * (-5 + x)
2(11(-5 + x) + x(-5 + x)) = x(x + 11) + 100
2((-5 * 11 + x * 11) + x(-5 + x)) = x(x + 11) + 100
2((-55 + 11x) + x(-5 + x)) = x(x + 11) + 100
2(-55 + 11x + (-5 * x + x * x)) = x(x + 11) + 100
2(-55 + 11x + (-5x + x2)) = x(x + 11) + 100

Combine like terms: 11x + -5x = 6x
2(-55 + 6x + x2) = x(x + 11) + 100
(-55 * 2 + 6x * 2 + x2 * 2) = x(x + 11) + 100
(-110 + 12x + 2x2) = x(x + 11) + 100

Reorder the terms:
-110 + 12x + 2x2 = x(11 + x) + 100
-110 + 12x + 2x2 = (11 * x + x * x) + 100
-110 + 12x + 2x2 = (11x + x2) + 100

Reorder the terms:
-110 + 12x + 2x2 = 100 + 11x + x2

Solving
-110 + 12x + 2x2 = 100 + 11x + x2

Solving for variable 'x'.

Reorder the terms:
-110 + -100 + 12x + -11x + 2x2 + -1x2 = 100 + 11x + x2 + -100 + -11x + -1x2

Combine like terms: -110 + -100 = -210
-210 + 12x + -11x + 2x2 + -1x2 = 100 + 11x + x2 + -100 + -11x + -1x2

Combine like terms: 12x + -11x = 1x
-210 + 1x + 2x2 + -1x2 = 100 + 11x + x2 + -100 + -11x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
-210 + 1x + 1x2 = 100 + 11x + x2 + -100 + -11x + -1x2

Reorder the terms:
-210 + 1x + 1x2 = 100 + -100 + 11x + -11x + x2 + -1x2

Combine like terms: 100 + -100 = 0
-210 + 1x + 1x2 = 0 + 11x + -11x + x2 + -1x2
-210 + 1x + 1x2 = 11x + -11x + x2 + -1x2

Combine like terms: 11x + -11x = 0
-210 + 1x + 1x2 = 0 + x2 + -1x2
-210 + 1x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-210 + 1x + 1x2 = 0

Factor a trinomial.
(-15 + -1x)(14 + -1x) = 0


Subproblem 1
Set the factor '(-15 + -1x)' equal to zero and attempt to solve:

Simplifying
-15 + -1x = 0

Solving
-15 + -1x = 0

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

Add '15' to each side of the equation.
-15 + 15 + -1x = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -1x = 0 + 15
-1x = 0 + 15

Combine like terms: 0 + 15 = 15
-1x = 15

Divide each side by '-1'.
x = -15

Simplifying
x = -15

Subproblem 2
Set the factor '(14 + -1x)' equal to zero and attempt to solve:

Simplifying
14 + -1x = 0

Solving
14 + -1x = 0

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

Add '-14' to each side of the equation.
14 + -14 + -1x = 0 + -14

Combine like terms: 14 + -14 = 0
0 + -1x = 0 + -14
-1x = 0 + -14

Combine like terms: 0 + -14 = -14
-1x = -14

Divide each side by '-1'.
x = 14

Simplifying
x = 14
Solution
x = {-15, 14}

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