0=x^2+7x-78

Solution for 0=x^2+7x-78 equation:

Simplifying
0 = x2 + 7x + -78

Reorder the terms:
0 = -78 + 7x + x2

Solving
0 = -78 + 7x + x2

Solving for variable 'x'.

Combine like terms: 0 + 78 = 78
78 + -7x + -1x2 = -78 + 7x + x2 + 78 + -7x + -1x2

Reorder the terms:
78 + -7x + -1x2 = -78 + 78 + 7x + -7x + x2 + -1x2

Combine like terms: -78 + 78 = 0
78 + -7x + -1x2 = 0 + 7x + -7x + x2 + -1x2
78 + -7x + -1x2 = 7x + -7x + x2 + -1x2

Combine like terms: 7x + -7x = 0
78 + -7x + -1x2 = 0 + x2 + -1x2
78 + -7x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
78 + -7x + -1x2 = 0

Factor a trinomial.
(6 + -1x)(13 + x) = 0

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

Simplifying
6 + -1x = 0

Solving
6 + -1x = 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 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Subproblem 2
Set the factor '(13 + x)' equal to zero and attempt to solve:

Simplifying
13 + x = 0

Solving
13 + x = 0

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

Add '-13' to each side of the equation.
13 + -13 + x = 0 + -13

Combine like terms: 13 + -13 = 0
0 + x = 0 + -13
x = 0 + -13

Combine like terms: 0 + -13 = -13
x = -13

Simplifying
x = -13
Solution
x = {6, -13}