2x+9=(13-x)(13-x)

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Solution for 2x+9=(13-x)(13-x) equation: 


Simplifying
2x + 9 = (13 + -1x)(13 + -1x)

Reorder the terms:
9 + 2x = (13 + -1x)(13 + -1x)

Multiply (13 + -1x) * (13 + -1x)
9 + 2x = (13(13 + -1x) + -1x * (13 + -1x))
9 + 2x = ((13 * 13 + -1x * 13) + -1x * (13 + -1x))
9 + 2x = ((169 + -13x) + -1x * (13 + -1x))
9 + 2x = (169 + -13x + (13 * -1x + -1x * -1x))
9 + 2x = (169 + -13x + (-13x + 1x2))

Combine like terms: -13x + -13x = -26x
9 + 2x = (169 + -26x + 1x2)

Solving
9 + 2x = 169 + -26x + 1x2

Solving for variable 'x'.

Reorder the terms:
9 + -169 + 2x + 26x + -1x2 = 169 + -26x + 1x2 + -169 + 26x + -1x2

Combine like terms: 9 + -169 = -160
-160 + 2x + 26x + -1x2 = 169 + -26x + 1x2 + -169 + 26x + -1x2

Combine like terms: 2x + 26x = 28x
-160 + 28x + -1x2 = 169 + -26x + 1x2 + -169 + 26x + -1x2

Reorder the terms:
-160 + 28x + -1x2 = 169 + -169 + -26x + 26x + 1x2 + -1x2

Combine like terms: 169 + -169 = 0
-160 + 28x + -1x2 = 0 + -26x + 26x + 1x2 + -1x2
-160 + 28x + -1x2 = -26x + 26x + 1x2 + -1x2

Combine like terms: -26x + 26x = 0
-160 + 28x + -1x2 = 0 + 1x2 + -1x2
-160 + 28x + -1x2 = 1x2 + -1x2

Combine like terms: 1x2 + -1x2 = 0
-160 + 28x + -1x2 = 0

Factor a trinomial.
(-20 + x)(8 + -1x) = 0


Subproblem 1
Set the factor '(-20 + x)' equal to zero and attempt to solve:

Simplifying
-20 + x = 0

Solving
-20 + x = 0

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

Add '20' to each side of the equation.
-20 + 20 + x = 0 + 20

Combine like terms: -20 + 20 = 0
0 + x = 0 + 20
x = 0 + 20

Combine like terms: 0 + 20 = 20
x = 20

Simplifying
x = 20

Subproblem 2
Set the factor '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {20, 8}

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