4w^2+5=9w

Solution for 4w^2+5=9w equation:

Simplifying
4w2 + 5 = 9w

Reorder the terms:
5 + 4w2 = 9w

Solving
5 + 4w2 = 9w

Solving for variable 'w'.

Reorder the terms:
5 + -9w + 4w2 = 9w + -9w

Combine like terms: 9w + -9w = 0
5 + -9w + 4w2 = 0

Factor a trinomial.
(1 + -1w)(5 + -4w) = 0

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

Simplifying
1 + -1w = 0

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

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

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

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

Simplifying
w = 1
Subproblem 2
Set the factor '(5 + -4w)' equal to zero and attempt to solve:

Simplifying
5 + -4w = 0

Solving
5 + -4w = 0

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

Add '-5' to each side of the equation.
5 + -5 + -4w = 0 + -5

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

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

Divide each side by '-4'.
w = 1.25

Simplifying
w = 1.25
Solution
w = {1, 1.25}