0=x^2-31x+150

Solution for 0=x^2-31x+150 equation:

Simplifying
0 = x2 + -31x + 150

Reorder the terms:
0 = 150 + -31x + x2

Solving
0 = 150 + -31x + x2

Solving for variable 'x'.

Combine like terms: 0 + -150 = -150
-150 + 31x + -1x2 = 150 + -31x + x2 + -150 + 31x + -1x2

Reorder the terms:
-150 + 31x + -1x2 = 150 + -150 + -31x + 31x + x2 + -1x2

Combine like terms: 150 + -150 = 0
-150 + 31x + -1x2 = 0 + -31x + 31x + x2 + -1x2
-150 + 31x + -1x2 = -31x + 31x + x2 + -1x2

Combine like terms: -31x + 31x = 0
-150 + 31x + -1x2 = 0 + x2 + -1x2
-150 + 31x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-150 + 31x + -1x2 = 0

Factor a trinomial.
(-25 + x)(6 + -1x) = 0

Subproblem 1
Set the factor '(-25 + x)' equal to zero and attempt to solve:

Simplifying
-25 + x = 0

Solving
-25 + x = 0

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

Add '25' to each side of the equation.
-25 + 25 + x = 0 + 25

Combine like terms: -25 + 25 = 0
0 + x = 0 + 25
x = 0 + 25

Combine like terms: 0 + 25 = 25
x = 25

Simplifying
x = 25
Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {25, 6}