x(x-17)=5(x-17)

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Solution for x(x-17)=5(x-17) equation: 


Simplifying
x(x + -17) = 5(x + -17)

Reorder the terms:
x(-17 + x) = 5(x + -17)
(-17 * x + x * x) = 5(x + -17)
(-17x + x2) = 5(x + -17)

Reorder the terms:
-17x + x2 = 5(-17 + x)
-17x + x2 = (-17 * 5 + x * 5)
-17x + x2 = (-85 + 5x)

Solving
-17x + x2 = -85 + 5x

Solving for variable 'x'.

Reorder the terms:
85 + -17x + -5x + x2 = -85 + 5x + 85 + -5x

Combine like terms: -17x + -5x = -22x
85 + -22x + x2 = -85 + 5x + 85 + -5x

Reorder the terms:
85 + -22x + x2 = -85 + 85 + 5x + -5x

Combine like terms: -85 + 85 = 0
85 + -22x + x2 = 0 + 5x + -5x
85 + -22x + x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
85 + -22x + x2 = 0

Factor a trinomial.
(5 + -1x)(17 + -1x) = 0


Subproblem 1
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5

Subproblem 2
Set the factor '(17 + -1x)' equal to zero and attempt to solve:

Simplifying
17 + -1x = 0

Solving
17 + -1x = 0

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

Add '-17' to each side of the equation.
17 + -17 + -1x = 0 + -17

Combine like terms: 17 + -17 = 0
0 + -1x = 0 + -17
-1x = 0 + -17

Combine like terms: 0 + -17 = -17
-1x = -17

Divide each side by '-1'.
x = 17

Simplifying
x = 17
Solution
x = {5, 17}

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