(6-w)(4w-5)=0

Solution for (6-w)(4w-5)=0 equation:

Simplifying
(6 + -1w)(4w + -5) = 0

Reorder the terms:
(6 + -1w)(-5 + 4w) = 0

Multiply (6 + -1w) * (-5 + 4w)
(6(-5 + 4w) + -1w * (-5 + 4w)) = 0
((-5 * 6 + 4w * 6) + -1w * (-5 + 4w)) = 0
((-30 + 24w) + -1w * (-5 + 4w)) = 0
(-30 + 24w + (-5 * -1w + 4w * -1w)) = 0
(-30 + 24w + (5w + -4w2)) = 0

Combine like terms: 24w + 5w = 29w
(-30 + 29w + -4w2) = 0

Solving
-30 + 29w + -4w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-6 + w)(5 + -4w) = 0

Subproblem 1
Set the factor '(-6 + w)' equal to zero and attempt to solve:

Simplifying
-6 + w = 0

Solving
-6 + w = 0

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

Add '6' to each side of the equation.
-6 + 6 + w = 0 + 6

Combine like terms: -6 + 6 = 0
0 + w = 0 + 6
w = 0 + 6

Combine like terms: 0 + 6 = 6
w = 6

Simplifying
w = 6
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 = {6, 1.25}