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

Solution for -4(w-9)(-w+1)=0 equation:

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

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

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

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

Combine like terms: 9w + 1w = 10w
-4(-9 + 10w + -1w2) = 0
(-9 * -4 + 10w * -4 + -1w2 * -4) = 0
(36 + -40w + 4w2) = 0

Solving
36 + -40w + 4w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '4'.
4(9 + -10w + w2) = 0

Factor a trinomial.
4((1 + -1w)(9 + -1w)) = 0

Ignore the factor 4.
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 '(9 + -1w)' equal to zero and attempt to solve:

Simplifying
9 + -1w = 0

Solving
9 + -1w = 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 + -1w = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1w = 0 + -9
-1w = 0 + -9

Combine like terms: 0 + -9 = -9
-1w = -9

Divide each side by '-1'.
w = 9

Simplifying
w = 9
Solution
w = {1, 9}