4w^2=-5w+6

Solution for 4w^2=-5w+6 equation:

Simplifying
4w2 = -5w + 6

Reorder the terms:
4w2 = 6 + -5w

Solving
4w2 = 6 + -5w

Solving for variable 'w'.

Reorder the terms:
-6 + 5w + 4w2 = 6 + -5w + -6 + 5w

Reorder the terms:
-6 + 5w + 4w2 = 6 + -6 + -5w + 5w

Combine like terms: 6 + -6 = 0
-6 + 5w + 4w2 = 0 + -5w + 5w
-6 + 5w + 4w2 = -5w + 5w

Combine like terms: -5w + 5w = 0
-6 + 5w + 4w2 = 0

Factor a trinomial.
(-2 + -1w)(3 + -4w) = 0

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

Simplifying
-2 + -1w = 0

Solving
-2 + -1w = 0

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

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

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

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

Divide each side by '-1'.
w = -2

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

Simplifying
3 + -4w = 0

Solving
3 + -4w = 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 + -4w = 0 + -3

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

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

Divide each side by '-4'.
w = 0.75

Simplifying
w = 0.75
Solution
w = {-2, 0.75}