8x(x+7)=x-42

Solution for 8x(x+7)=x-42 equation:

Simplifying
8x(x + 7) = x + -42

Reorder the terms:
8x(7 + x) = x + -42
(7 * 8x + x * 8x) = x + -42
(56x + 8x2) = x + -42

Reorder the terms:
56x + 8x2 = -42 + x

Solving
56x + 8x2 = -42 + x

Solving for variable 'x'.

Reorder the terms:
42 + 56x + -1x + 8x2 = -42 + x + 42 + -1x

Combine like terms: 56x + -1x = 55x
42 + 55x + 8x2 = -42 + x + 42 + -1x

Reorder the terms:
42 + 55x + 8x2 = -42 + 42 + x + -1x

Combine like terms: -42 + 42 = 0
42 + 55x + 8x2 = 0 + x + -1x
42 + 55x + 8x2 = x + -1x

Combine like terms: x + -1x = 0
42 + 55x + 8x2 = 0

Factor a trinomial.
(6 + x)(7 + 8x) = 0

Subproblem 1
Set the factor '(6 + x)' equal to zero and attempt to solve:

Simplifying
6 + x = 0

Solving
6 + x = 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 + x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + x = 0 + -6
x = 0 + -6

Combine like terms: 0 + -6 = -6
x = -6

Simplifying
x = -6
Subproblem 2
Set the factor '(7 + 8x)' equal to zero and attempt to solve:

Simplifying
7 + 8x = 0

Solving
7 + 8x = 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 + 8x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 8x = 0 + -7
8x = 0 + -7

Combine like terms: 0 + -7 = -7
8x = -7

Divide each side by '8'.
x = -0.875

Simplifying
x = -0.875
Solution
x = {-6, -0.875}