0=x^2-18x+80

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Solution for 0=x^2-18x+80 equation: 


Simplifying
0 = x2 + -18x + 80

Reorder the terms:
0 = 80 + -18x + x2

Solving
0 = 80 + -18x + x2

Solving for variable 'x'.

Combine like terms: 0 + -80 = -80
-80 + 18x + -1x2 = 80 + -18x + x2 + -80 + 18x + -1x2

Reorder the terms:
-80 + 18x + -1x2 = 80 + -80 + -18x + 18x + x2 + -1x2

Combine like terms: 80 + -80 = 0
-80 + 18x + -1x2 = 0 + -18x + 18x + x2 + -1x2
-80 + 18x + -1x2 = -18x + 18x + x2 + -1x2

Combine like terms: -18x + 18x = 0
-80 + 18x + -1x2 = 0 + x2 + -1x2
-80 + 18x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-80 + 18x + -1x2 = 0

Factor a trinomial.
(-10 + x)(8 + -1x) = 0


Subproblem 1
Set the factor '(-10 + x)' equal to zero and attempt to solve:

Simplifying
-10 + x = 0

Solving
-10 + x = 0

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

Add '10' to each side of the equation.
-10 + 10 + x = 0 + 10

Combine like terms: -10 + 10 = 0
0 + x = 0 + 10
x = 0 + 10

Combine like terms: 0 + 10 = 10
x = 10

Simplifying
x = 10

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 = {10, 8}

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