(x+6)(x-1)=78

Solution for (x+6)(x-1)=78 equation:

Simplifying
(x + 6)(x + -1) = 78

Reorder the terms:
(6 + x)(x + -1) = 78

Reorder the terms:
(6 + x)(-1 + x) = 78

Multiply (6 + x) * (-1 + x)
(6(-1 + x) + x(-1 + x)) = 78
((-1 * 6 + x * 6) + x(-1 + x)) = 78
((-6 + 6x) + x(-1 + x)) = 78
(-6 + 6x + (-1 * x + x * x)) = 78
(-6 + 6x + (-1x + x2)) = 78

Combine like terms: 6x + -1x = 5x
(-6 + 5x + x2) = 78

Solving
-6 + 5x + x2 = 78

Solving for variable 'x'.

Reorder the terms:
-6 + -78 + 5x + x2 = 78 + -78

Combine like terms: -6 + -78 = -84
-84 + 5x + x2 = 78 + -78

Combine like terms: 78 + -78 = 0
-84 + 5x + x2 = 0

Factor a trinomial.
(-12 + -1x)(7 + -1x) = 0

Subproblem 1
Set the factor '(-12 + -1x)' equal to zero and attempt to solve:

Simplifying
-12 + -1x = 0

Solving
-12 + -1x = 0

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

Add '12' to each side of the equation.
-12 + 12 + -1x = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -1x = 0 + 12
-1x = 0 + 12

Combine like terms: 0 + 12 = 12
-1x = 12

Divide each side by '-1'.
x = -12

Simplifying
x = -12
Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

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

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

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {-12, 7}