8990=x^2-20x+65

Solution for 8990=x^2-20x+65 equation:

Simplifying
8990 = x2 + -20x + 65

Reorder the terms:
8990 = 65 + -20x + x2

Solving
8990 = 65 + -20x + x2

Solving for variable 'x'.

Combine like terms: 8990 + -65 = 8925
8925 + 20x + -1x2 = 65 + -20x + x2 + -65 + 20x + -1x2

Reorder the terms:
8925 + 20x + -1x2 = 65 + -65 + -20x + 20x + x2 + -1x2

Combine like terms: 65 + -65 = 0
8925 + 20x + -1x2 = 0 + -20x + 20x + x2 + -1x2
8925 + 20x + -1x2 = -20x + 20x + x2 + -1x2

Combine like terms: -20x + 20x = 0
8925 + 20x + -1x2 = 0 + x2 + -1x2
8925 + 20x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
8925 + 20x + -1x2 = 0

Factor a trinomial.
(105 + -1x)(85 + x) = 0

Subproblem 1
Set the factor '(105 + -1x)' equal to zero and attempt to solve:

Simplifying
105 + -1x = 0

Solving
105 + -1x = 0

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

Add '-105' to each side of the equation.
105 + -105 + -1x = 0 + -105

Combine like terms: 105 + -105 = 0
0 + -1x = 0 + -105
-1x = 0 + -105

Combine like terms: 0 + -105 = -105
-1x = -105

Divide each side by '-1'.
x = 105

Simplifying
x = 105
Subproblem 2
Set the factor '(85 + x)' equal to zero and attempt to solve:

Simplifying
85 + x = 0

Solving
85 + x = 0

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

Add '-85' to each side of the equation.
85 + -85 + x = 0 + -85

Combine like terms: 85 + -85 = 0
0 + x = 0 + -85
x = 0 + -85

Combine like terms: 0 + -85 = -85
x = -85

Simplifying
x = -85
Solution
x = {105, -85}