-7x=(x+1)(x-12)

Solution for -7x=(x+1)(x-12) equation:

Simplifying
-7x = (x + 1)(x + -12)

Reorder the terms:
-7x = (1 + x)(x + -12)

Reorder the terms:
-7x = (1 + x)(-12 + x)

Multiply (1 + x) * (-12 + x)
-7x = (1(-12 + x) + x(-12 + x))
-7x = ((-12 * 1 + x * 1) + x(-12 + x))
-7x = ((-12 + 1x) + x(-12 + x))
-7x = (-12 + 1x + (-12 * x + x * x))
-7x = (-12 + 1x + (-12x + x2))

Combine like terms: 1x + -12x = -11x
-7x = (-12 + -11x + x2)

Solving
-7x = -12 + -11x + x2

Solving for variable 'x'.

Reorder the terms:
12 + -7x + 11x + -1x2 = -12 + -11x + x2 + 12 + 11x + -1x2

Combine like terms: -7x + 11x = 4x
12 + 4x + -1x2 = -12 + -11x + x2 + 12 + 11x + -1x2

Reorder the terms:
12 + 4x + -1x2 = -12 + 12 + -11x + 11x + x2 + -1x2

Combine like terms: -12 + 12 = 0
12 + 4x + -1x2 = 0 + -11x + 11x + x2 + -1x2
12 + 4x + -1x2 = -11x + 11x + x2 + -1x2

Combine like terms: -11x + 11x = 0
12 + 4x + -1x2 = 0 + x2 + -1x2
12 + 4x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
12 + 4x + -1x2 = 0

Factor a trinomial.
(6 + -1x)(2 + 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 '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 0

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

Add '-2' to each side of the equation.
2 + -2 + x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

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