3x(x+1)-2x(x-5)=-42

Solution for 3x(x+1)-2x(x-5)=-42 equation:

Simplifying
3x(x + 1) + -2x(x + -5) = -42

Reorder the terms:
3x(1 + x) + -2x(x + -5) = -42
(1 * 3x + x * 3x) + -2x(x + -5) = -42
(3x + 3x2) + -2x(x + -5) = -42

Reorder the terms:
3x + 3x2 + -2x(-5 + x) = -42
3x + 3x2 + (-5 * -2x + x * -2x) = -42
3x + 3x2 + (10x + -2x2) = -42

Reorder the terms:
3x + 10x + 3x2 + -2x2 = -42

Combine like terms: 3x + 10x = 13x
13x + 3x2 + -2x2 = -42

Combine like terms: 3x2 + -2x2 = 1x2
13x + 1x2 = -42

Solving
13x + 1x2 = -42

Solving for variable 'x'.

Reorder the terms:
42 + 13x + 1x2 = -42 + 42

Combine like terms: -42 + 42 = 0
42 + 13x + 1x2 = 0

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

Subproblem 1
Set the factor '(7 + x)' equal to zero and attempt to solve:

Simplifying
7 + x = 0

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

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

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

Simplifying
x = -7
Subproblem 2
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
Solution
x = {-7, -6}