8u^2+32u=-14

Solution for 8u^2+32u=-14 equation:

Simplifying
8u2 + 32u = -14

Reorder the terms:
32u + 8u2 = -14

Solving
32u + 8u2 = -14

Solving for variable 'u'.

Reorder the terms:
14 + 32u + 8u2 = -14 + 14

Combine like terms: -14 + 14 = 0
14 + 32u + 8u2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(7 + 16u + 4u2) = 0

Factor a trinomial.
2((7 + 2u)(1 + 2u)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(7 + 2u)' equal to zero and attempt to solve:

Simplifying
7 + 2u = 0

Solving
7 + 2u = 0

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

Add '-7' to each side of the equation.
7 + -7 + 2u = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 2u = 0 + -7
2u = 0 + -7

Combine like terms: 0 + -7 = -7
2u = -7

Divide each side by '2'.
u = -3.5

Simplifying
u = -3.5
Subproblem 2
Set the factor '(1 + 2u)' equal to zero and attempt to solve:

Simplifying
1 + 2u = 0

Solving
1 + 2u = 0

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

Add '-1' to each side of the equation.
1 + -1 + 2u = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2u = 0 + -1
2u = 0 + -1

Combine like terms: 0 + -1 = -1
2u = -1

Divide each side by '2'.
u = -0.5

Simplifying
u = -0.5
Solution
u = {-3.5, -0.5}