2w(4w-9)=5

Solution for 2w(4w-9)=5 equation:

Simplifying
2w(4w + -9) = 5

Reorder the terms:
2w(-9 + 4w) = 5
(-9 * 2w + 4w * 2w) = 5
(-18w + 8w2) = 5

Solving
-18w + 8w2 = 5

Solving for variable 'w'.

Reorder the terms:
-5 + -18w + 8w2 = 5 + -5

Combine like terms: 5 + -5 = 0
-5 + -18w + 8w2 = 0

Factor a trinomial.
(-1 + -4w)(5 + -2w) = 0

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

Simplifying
5 + -2w = 0

Solving
5 + -2w = 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 + -2w = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2w = 0 + -5
-2w = 0 + -5

Combine like terms: 0 + -5 = -5
-2w = -5

Divide each side by '-2'.
w = 2.5

Simplifying
w = 2.5
Solution
w = {-0.25, 2.5}