0=x^2-19x+90

Solution for 0=x^2-19x+90 equation:

Simplifying
0 = x2 + -19x + 90

Reorder the terms:
0 = 90 + -19x + x2

Solving
0 = 90 + -19x + x2

Solving for variable 'x'.

Combine like terms: 0 + -90 = -90
-90 + 19x + -1x2 = 90 + -19x + x2 + -90 + 19x + -1x2

Reorder the terms:
-90 + 19x + -1x2 = 90 + -90 + -19x + 19x + x2 + -1x2

Combine like terms: 90 + -90 = 0
-90 + 19x + -1x2 = 0 + -19x + 19x + x2 + -1x2
-90 + 19x + -1x2 = -19x + 19x + x2 + -1x2

Combine like terms: -19x + 19x = 0
-90 + 19x + -1x2 = 0 + x2 + -1x2
-90 + 19x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-90 + 19x + -1x2 = 0

Factor a trinomial.
(-10 + x)(9 + -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 '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

Solving
9 + -1x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1x = 0 + -9
-1x = 0 + -9

Combine like terms: 0 + -9 = -9
-1x = -9

Divide each side by '-1'.
x = 9

Simplifying
x = 9
Solution
x = {10, 9}