x(x+2)=15x-22

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Solution for x(x+2)=15x-22 equation: 


Simplifying
x(x + 2) = 15x + -22

Reorder the terms:
x(2 + x) = 15x + -22
(2 * x + x * x) = 15x + -22
(2x + x2) = 15x + -22

Reorder the terms:
2x + x2 = -22 + 15x

Solving
2x + x2 = -22 + 15x

Solving for variable 'x'.

Reorder the terms:
22 + 2x + -15x + x2 = -22 + 15x + 22 + -15x

Combine like terms: 2x + -15x = -13x
22 + -13x + x2 = -22 + 15x + 22 + -15x

Reorder the terms:
22 + -13x + x2 = -22 + 22 + 15x + -15x

Combine like terms: -22 + 22 = 0
22 + -13x + x2 = 0 + 15x + -15x
22 + -13x + x2 = 15x + -15x

Combine like terms: 15x + -15x = 0
22 + -13x + x2 = 0

Factor a trinomial.
(2 + -1x)(11 + -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 '(11 + -1x)' equal to zero and attempt to solve:

Simplifying
11 + -1x = 0

Solving
11 + -1x = 0

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

Add '-11' to each side of the equation.
11 + -11 + -1x = 0 + -11

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

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

Divide each side by '-1'.
x = 11

Simplifying
x = 11
Solution
x = {2, 11}

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