4x^2+31x=-42

Solution for 4x^2+31x=-42 equation:

Simplifying
4x2 + 31x = -42

Reorder the terms:
31x + 4x2 = -42

Solving
31x + 4x2 = -42

Solving for variable 'x'.

Reorder the terms:
42 + 31x + 4x2 = -42 + 42

Combine like terms: -42 + 42 = 0
42 + 31x + 4x2 = 0

Factor a trinomial.
(6 + x)(7 + 4x) = 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 + 4x)' equal to zero and attempt to solve:

Simplifying
7 + 4x = 0

Solving
7 + 4x = 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 + 4x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 4x = 0 + -7
4x = 0 + -7

Combine like terms: 0 + -7 = -7
4x = -7

Divide each side by '4'.
x = -1.75

Simplifying
x = -1.75
Solution
x = {-6, -1.75}