7x^2-57x+108=0

Solution for 7x^2-57x+108=0 equation:

Simplifying
7x2 + -57x + 108 = 0

Reorder the terms:
108 + -57x + 7x2 = 0

Solving
108 + -57x + 7x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(3 + -1x)(36 + -7x) = 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 '(36 + -7x)' equal to zero and attempt to solve:

Simplifying
36 + -7x = 0

Solving
36 + -7x = 0

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

Add '-36' to each side of the equation.
36 + -36 + -7x = 0 + -36

Combine like terms: 36 + -36 = 0
0 + -7x = 0 + -36
-7x = 0 + -36

Combine like terms: 0 + -36 = -36
-7x = -36

Divide each side by '-7'.
x = 5.142857143

Simplifying
x = 5.142857143
Solution
x = {3, 5.142857143}