x^2+7x-78=42

Solution for x^2+7x-78=42 equation:

Simplifying
x2 + 7x + -78 = 42

Reorder the terms:
-78 + 7x + x2 = 42

Solving
-78 + 7x + x2 = 42

Solving for variable 'x'.

Reorder the terms:
-78 + -42 + 7x + x2 = 42 + -42

Combine like terms: -78 + -42 = -120
-120 + 7x + x2 = 42 + -42

Combine like terms: 42 + -42 = 0
-120 + 7x + x2 = 0

Factor a trinomial.
(-15 + -1x)(8 + -1x) = 0

Subproblem 1
Set the factor '(-15 + -1x)' equal to zero and attempt to solve:

Simplifying
-15 + -1x = 0

Solving
-15 + -1x = 0

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

Add '15' to each side of the equation.
-15 + 15 + -1x = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -1x = 0 + 15
-1x = 0 + 15

Combine like terms: 0 + 15 = 15
-1x = 15

Divide each side by '-1'.
x = -15

Simplifying
x = -15
Subproblem 2
Set the factor '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {-15, 8}