0=x^2-185x+7800

Solution for 0=x^2-185x+7800 equation:

Simplifying
0 = x2 + -185x + 7800

Reorder the terms:
0 = 7800 + -185x + x2

Solving
0 = 7800 + -185x + x2

Solving for variable 'x'.

Combine like terms: 0 + -7800 = -7800
-7800 + 185x + -1x2 = 7800 + -185x + x2 + -7800 + 185x + -1x2

Reorder the terms:
-7800 + 185x + -1x2 = 7800 + -7800 + -185x + 185x + x2 + -1x2

Combine like terms: 7800 + -7800 = 0
-7800 + 185x + -1x2 = 0 + -185x + 185x + x2 + -1x2
-7800 + 185x + -1x2 = -185x + 185x + x2 + -1x2

Combine like terms: -185x + 185x = 0
-7800 + 185x + -1x2 = 0 + x2 + -1x2
-7800 + 185x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-7800 + 185x + -1x2 = 0

Factor a trinomial.
(-120 + x)(65 + -1x) = 0

Subproblem 1
Set the factor '(-120 + x)' equal to zero and attempt to solve:

Simplifying
-120 + x = 0

Solving
-120 + x = 0

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

Add '120' to each side of the equation.
-120 + 120 + x = 0 + 120

Combine like terms: -120 + 120 = 0
0 + x = 0 + 120
x = 0 + 120

Combine like terms: 0 + 120 = 120
x = 120

Simplifying
x = 120
Subproblem 2
Set the factor '(65 + -1x)' equal to zero and attempt to solve:

Simplifying
65 + -1x = 0

Solving
65 + -1x = 0

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

Add '-65' to each side of the equation.
65 + -65 + -1x = 0 + -65

Combine like terms: 65 + -65 = 0
0 + -1x = 0 + -65
-1x = 0 + -65

Combine like terms: 0 + -65 = -65
-1x = -65

Divide each side by '-1'.
x = 65

Simplifying
x = 65
Solution
x = {120, 65}