5x^2+31x+5=-1

Solution for 5x^2+31x+5=-1 equation:

Simplifying
5x2 + 31x + 5 = -1

Reorder the terms:
5 + 31x + 5x2 = -1

Solving
5 + 31x + 5x2 = -1

Solving for variable 'x'.

Reorder the terms:
5 + 1 + 31x + 5x2 = -1 + 1

Combine like terms: 5 + 1 = 6
6 + 31x + 5x2 = -1 + 1

Combine like terms: -1 + 1 = 0
6 + 31x + 5x2 = 0

Factor a trinomial.
(6 + x)(1 + 5x) = 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 '(1 + 5x)' equal to zero and attempt to solve:

Simplifying
1 + 5x = 0

Solving
1 + 5x = 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 + 5x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 5x = 0 + -1
5x = 0 + -1

Combine like terms: 0 + -1 = -1
5x = -1

Divide each side by '5'.
x = -0.2

Simplifying
x = -0.2
Solution
x = {-6, -0.2}