x(x-1)=5(2x+3)+11

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Solution for x(x-1)=5(2x+3)+11 equation: 


Simplifying
x(x + -1) = 5(2x + 3) + 11

Reorder the terms:
x(-1 + x) = 5(2x + 3) + 11
(-1 * x + x * x) = 5(2x + 3) + 11
(-1x + x2) = 5(2x + 3) + 11

Reorder the terms:
-1x + x2 = 5(3 + 2x) + 11
-1x + x2 = (3 * 5 + 2x * 5) + 11
-1x + x2 = (15 + 10x) + 11

Reorder the terms:
-1x + x2 = 15 + 11 + 10x

Combine like terms: 15 + 11 = 26
-1x + x2 = 26 + 10x

Solving
-1x + x2 = 26 + 10x

Solving for variable 'x'.

Reorder the terms:
-26 + -1x + -10x + x2 = 26 + 10x + -26 + -10x

Combine like terms: -1x + -10x = -11x
-26 + -11x + x2 = 26 + 10x + -26 + -10x

Reorder the terms:
-26 + -11x + x2 = 26 + -26 + 10x + -10x

Combine like terms: 26 + -26 = 0
-26 + -11x + x2 = 0 + 10x + -10x
-26 + -11x + x2 = 10x + -10x

Combine like terms: 10x + -10x = 0
-26 + -11x + x2 = 0

Factor a trinomial.
(-2 + -1x)(13 + -1x) = 0


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

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1x = 0 + 2

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

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

Divide each side by '-1'.
x = -2

Simplifying
x = -2

Subproblem 2
Set the factor '(13 + -1x)' equal to zero and attempt to solve:

Simplifying
13 + -1x = 0

Solving
13 + -1x = 0

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

Add '-13' to each side of the equation.
13 + -13 + -1x = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -1x = 0 + -13
-1x = 0 + -13

Combine like terms: 0 + -13 = -13
-1x = -13

Divide each side by '-1'.
x = 13

Simplifying
x = 13
Solution
x = {-2, 13}

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