8x^2+31x+21=0

Solution for 8x^2+31x+21=0 equation:

Simplifying
8x2 + 31x + 21 = 0

Reorder the terms:
21 + 31x + 8x2 = 0

Solving
21 + 31x + 8x2 = 0

Solving for variable 'x'.

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

Subproblem 1
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 0

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

Add '-3' to each side of the equation.
3 + -3 + x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3

Combine like terms: 0 + -3 = -3
x = -3

Simplifying
x = -3
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 = {-3, -0.875}