5w^2+4w-57=0

Solution for 5w^2+4w-57=0 equation:

Simplifying
5w2 + 4w + -57 = 0

Reorder the terms:
-57 + 4w + 5w2 = 0

Solving
-57 + 4w + 5w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-19 + -5w)(3 + -1w) = 0

Subproblem 1
Set the factor '(-19 + -5w)' equal to zero and attempt to solve:

Simplifying
-19 + -5w = 0

Solving
-19 + -5w = 0

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

Add '19' to each side of the equation.
-19 + 19 + -5w = 0 + 19

Combine like terms: -19 + 19 = 0
0 + -5w = 0 + 19
-5w = 0 + 19

Combine like terms: 0 + 19 = 19
-5w = 19

Divide each side by '-5'.
w = -3.8

Simplifying
w = -3.8
Subproblem 2
Set the factor '(3 + -1w)' equal to zero and attempt to solve:

Simplifying
3 + -1w = 0

Solving
3 + -1w = 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 + -1w = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1w = 0 + -3
-1w = 0 + -3

Combine like terms: 0 + -3 = -3
-1w = -3

Divide each side by '-1'.
w = 3

Simplifying
w = 3
Solution
w = {-3.8, 3}