4u^2+3=-8u

Solution for 4u^2+3=-8u equation:

Simplifying
4u2 + 3 = -8u

Reorder the terms:
3 + 4u2 = -8u

Solving
3 + 4u2 = -8u

Solving for variable 'u'.

Reorder the terms:
3 + 8u + 4u2 = -8u + 8u

Combine like terms: -8u + 8u = 0
3 + 8u + 4u2 = 0

Factor a trinomial.
(3 + 2u)(1 + 2u) = 0

Subproblem 1
Set the factor '(3 + 2u)' equal to zero and attempt to solve:

Simplifying
3 + 2u = 0

Solving
3 + 2u = 0

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

Add '-3' to each side of the equation.
3 + -3 + 2u = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2u = 0 + -3
2u = 0 + -3

Combine like terms: 0 + -3 = -3
2u = -3

Divide each side by '2'.
u = -1.5

Simplifying
u = -1.5
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 = {-1.5, -0.5}