4w^2+3=-8w

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

Simplifying
4w2 + 3 = -8w

Reorder the terms:
3 + 4w2 = -8w

Solving
3 + 4w2 = -8w

Solving for variable 'w'.

Reorder the terms:
3 + 8w + 4w2 = -8w + 8w

Combine like terms: -8w + 8w = 0
3 + 8w + 4w2 = 0

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

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

Simplifying
3 + 2w = 0

Solving
3 + 2w = 0

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

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

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

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

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

Simplifying
w = -1.5
Subproblem 2
Set the factor '(1 + 2w)' equal to zero and attempt to solve:

Simplifying
1 + 2w = 0

Solving
1 + 2w = 0

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

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

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

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

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

Simplifying
w = -0.5
Solution
w = {-1.5, -0.5}