5w^2+3=-8w

Solution for 5w^2+3=-8w equation:

Simplifying
5w2 + 3 = -8w

Reorder the terms:
3 + 5w2 = -8w

Solving
3 + 5w2 = -8w

Solving for variable 'w'.

Reorder the terms:
3 + 8w + 5w2 = -8w + 8w

Combine like terms: -8w + 8w = 0
3 + 8w + 5w2 = 0

Factor a trinomial.
(1 + w)(3 + 5w) = 0

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

Simplifying
1 + w = 0

Solving
1 + w = 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 + w = 0 + -1

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

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

Simplifying
w = -1
Subproblem 2
Set the factor '(3 + 5w)' equal to zero and attempt to solve:

Simplifying
3 + 5w = 0

Solving
3 + 5w = 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 + 5w = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 5w = 0 + -3
5w = 0 + -3

Combine like terms: 0 + -3 = -3
5w = -3

Divide each side by '5'.
w = -0.6

Simplifying
w = -0.6
Solution
w = {-1, -0.6}