(x+6)(x-7)=-42

Solution for (x+6)(x-7)=-42 equation:

Simplifying
(x + 6)(x + -7) = -42

Reorder the terms:
(6 + x)(x + -7) = -42

Reorder the terms:
(6 + x)(-7 + x) = -42

Multiply (6 + x) * (-7 + x)
(6(-7 + x) + x(-7 + x)) = -42
((-7 * 6 + x * 6) + x(-7 + x)) = -42
((-42 + 6x) + x(-7 + x)) = -42
(-42 + 6x + (-7 * x + x * x)) = -42
(-42 + 6x + (-7x + x2)) = -42

Combine like terms: 6x + -7x = -1x
(-42 + -1x + x2) = -42

Add '42' to each side of the equation.
-42 + -1x + 42 + x2 = -42 + 42

Reorder the terms:
-42 + 42 + -1x + x2 = -42 + 42

Combine like terms: -42 + 42 = 0
0 + -1x + x2 = -42 + 42
-1x + x2 = -42 + 42

Combine like terms: -42 + 42 = 0
-1x + x2 = 0

Solving
-1x + x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-1 + x) = 0

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(-1 + x)' equal to zero and attempt to solve:

Simplifying
-1 + x = 0

Solving
-1 + x = 0

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

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

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

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

Simplifying
x = 1
Solution
x = {0, 1}