0=x^2-10x+24

Solution for 0=x^2-10x+24 equation:

Simplifying
0 = x2 + -10x + 24

Reorder the terms:
0 = 24 + -10x + x2

Solving
0 = 24 + -10x + x2

Solving for variable 'x'.

Combine like terms: 0 + -24 = -24
-24 + 10x + -1x2 = 24 + -10x + x2 + -24 + 10x + -1x2

Reorder the terms:
-24 + 10x + -1x2 = 24 + -24 + -10x + 10x + x2 + -1x2

Combine like terms: 24 + -24 = 0
-24 + 10x + -1x2 = 0 + -10x + 10x + x2 + -1x2
-24 + 10x + -1x2 = -10x + 10x + x2 + -1x2

Combine like terms: -10x + 10x = 0
-24 + 10x + -1x2 = 0 + x2 + -1x2
-24 + 10x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-24 + 10x + -1x2 = 0

Factor a trinomial.
(-6 + x)(4 + -1x) = 0

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

Simplifying
-6 + x = 0

Solving
-6 + x = 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 + x = 0 + 6

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

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

Simplifying
x = 6
Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {6, 4}