(3-w)(4w-9)=0

Solution for (3-w)(4w-9)=0 equation:

Simplifying
(3 + -1w)(4w + -9) = 0

Reorder the terms:
(3 + -1w)(-9 + 4w) = 0

Multiply (3 + -1w) * (-9 + 4w)
(3(-9 + 4w) + -1w * (-9 + 4w)) = 0
((-9 * 3 + 4w * 3) + -1w * (-9 + 4w)) = 0
((-27 + 12w) + -1w * (-9 + 4w)) = 0
(-27 + 12w + (-9 * -1w + 4w * -1w)) = 0
(-27 + 12w + (9w + -4w2)) = 0

Combine like terms: 12w + 9w = 21w
(-27 + 21w + -4w2) = 0

Solving
-27 + 21w + -4w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-3 + w)(9 + -4w) = 0

Subproblem 1
Set the factor '(-3 + w)' equal to zero and attempt to solve:

Simplifying
-3 + w = 0

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

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

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

Simplifying
w = 3
Subproblem 2
Set the factor '(9 + -4w)' equal to zero and attempt to solve:

Simplifying
9 + -4w = 0

Solving
9 + -4w = 0

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

Add '-9' to each side of the equation.
9 + -9 + -4w = 0 + -9

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

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

Divide each side by '-4'.
w = 2.25

Simplifying
w = 2.25
Solution
w = {3, 2.25}