10x^2-69x+117=0

Solution for 10x^2-69x+117=0 equation:

Simplifying
10x2 + -69x + 117 = 0

Reorder the terms:
117 + -69x + 10x2 = 0

Solving
117 + -69x + 10x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(3 + -1x)(39 + -10x) = 0

Subproblem 1
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Subproblem 2
Set the factor '(39 + -10x)' equal to zero and attempt to solve:

Simplifying
39 + -10x = 0

Solving
39 + -10x = 0

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

Add '-39' to each side of the equation.
39 + -39 + -10x = 0 + -39

Combine like terms: 39 + -39 = 0
0 + -10x = 0 + -39
-10x = 0 + -39

Combine like terms: 0 + -39 = -39
-10x = -39

Divide each side by '-10'.
x = 3.9

Simplifying
x = 3.9
Solution
x = {3, 3.9}