4w^2=-13w-3

Solution for 4w^2=-13w-3 equation:

Simplifying
4w2 = -13w + -3

Reorder the terms:
4w2 = -3 + -13w

Solving
4w2 = -3 + -13w

Solving for variable 'w'.

Reorder the terms:
3 + 13w + 4w2 = -3 + -13w + 3 + 13w

Reorder the terms:
3 + 13w + 4w2 = -3 + 3 + -13w + 13w

Combine like terms: -3 + 3 = 0
3 + 13w + 4w2 = 0 + -13w + 13w
3 + 13w + 4w2 = -13w + 13w

Combine like terms: -13w + 13w = 0
3 + 13w + 4w2 = 0

Factor a trinomial.
(3 + w)(1 + 4w) = 0

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

Simplifying
3 + w = 0

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

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

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

Simplifying
w = -3
Subproblem 2
Set the factor '(1 + 4w)' equal to zero and attempt to solve:

Simplifying
1 + 4w = 0

Solving
1 + 4w = 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 + 4w = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 4w = 0 + -1
4w = 0 + -1

Combine like terms: 0 + -1 = -1
4w = -1

Divide each side by '4'.
w = -0.25

Simplifying
w = -0.25
Solution
w = {-3, -0.25}