(x+7)(x)-78=0

Solution for (x+7)(x)-78=0 equation:

Simplifying
(x + 7)(x) + -78 = 0

Reorder the terms:
(7 + x)(x) + -78 = 0

Reorder the terms for easier multiplication:
x(7 + x) + -78 = 0
(7 * x + x * x) + -78 = 0
(7x + x2) + -78 = 0

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

Solving
-78 + 7x + x2 = 0

Solving for variable 'x'.

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

Subproblem 1
Set the factor '(-13 + -1x)' equal to zero and attempt to solve:

Simplifying
-13 + -1x = 0

Solving
-13 + -1x = 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 + -1x = 0 + 13

Combine like terms: -13 + 13 = 0
0 + -1x = 0 + 13
-1x = 0 + 13

Combine like terms: 0 + 13 = 13
-1x = 13

Divide each side by '-1'.
x = -13

Simplifying
x = -13
Subproblem 2
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
Solution
x = {-13, 6}