4w^2+3w-45=0

Solution for 4w^2+3w-45=0 equation:

Simplifying
4w2 + 3w + -45 = 0

Reorder the terms:
-45 + 3w + 4w2 = 0

Solving
-45 + 3w + 4w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-15 + -4w)(3 + -1w) = 0

Subproblem 1
Set the factor '(-15 + -4w)' equal to zero and attempt to solve:

Simplifying
-15 + -4w = 0

Solving
-15 + -4w = 0

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

Add '15' to each side of the equation.
-15 + 15 + -4w = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -4w = 0 + 15
-4w = 0 + 15

Combine like terms: 0 + 15 = 15
-4w = 15

Divide each side by '-4'.
w = -3.75

Simplifying
w = -3.75
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 = {-3.75, 3}