0=3042+x^2-117x

Solution for 0=3042+x^2-117x equation:

Simplifying
0 = 3042 + x2 + -117x

Reorder the terms:
0 = 3042 + -117x + x2

Solving
0 = 3042 + -117x + x2

Solving for variable 'x'.

Combine like terms: 0 + -3042 = -3042
-3042 + 117x + -1x2 = 3042 + -117x + x2 + -3042 + 117x + -1x2

Reorder the terms:
-3042 + 117x + -1x2 = 3042 + -3042 + -117x + 117x + x2 + -1x2

Combine like terms: 3042 + -3042 = 0
-3042 + 117x + -1x2 = 0 + -117x + 117x + x2 + -1x2
-3042 + 117x + -1x2 = -117x + 117x + x2 + -1x2

Combine like terms: -117x + 117x = 0
-3042 + 117x + -1x2 = 0 + x2 + -1x2
-3042 + 117x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-3042 + 117x + -1x2 = 0

Factor a trinomial.
(-78 + x)(39 + -1x) = 0

Subproblem 1
Set the factor '(-78 + x)' equal to zero and attempt to solve:

Simplifying
-78 + x = 0

Solving
-78 + x = 0

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

Add '78' to each side of the equation.
-78 + 78 + x = 0 + 78

Combine like terms: -78 + 78 = 0
0 + x = 0 + 78
x = 0 + 78

Combine like terms: 0 + 78 = 78
x = 78

Simplifying
x = 78
Subproblem 2
Set the factor '(39 + -1x)' equal to zero and attempt to solve:

Simplifying
39 + -1x = 0

Solving
39 + -1x = 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 + -1x = 0 + -39

Combine like terms: 39 + -39 = 0
0 + -1x = 0 + -39
-1x = 0 + -39

Combine like terms: 0 + -39 = -39
-1x = -39

Divide each side by '-1'.
x = 39

Simplifying
x = 39
Solution
x = {78, 39}