0=(4w+2)(9-w)

Solution for 0=(4w+2)(9-w) equation:

Simplifying
0 = (4w + 2)(9 + -1w)

Reorder the terms:
0 = (2 + 4w)(9 + -1w)

Multiply (2 + 4w) * (9 + -1w)
0 = (2(9 + -1w) + 4w * (9 + -1w))
0 = ((9 * 2 + -1w * 2) + 4w * (9 + -1w))
0 = ((18 + -2w) + 4w * (9 + -1w))
0 = (18 + -2w + (9 * 4w + -1w * 4w))
0 = (18 + -2w + (36w + -4w2))

Combine like terms: -2w + 36w = 34w
0 = (18 + 34w + -4w2)

Solving
0 = 18 + 34w + -4w2

Solving for variable 'w'.

Combine like terms: 0 + -18 = -18
-18 + -34w + 4w2 = 18 + 34w + -4w2 + -18 + -34w + 4w2

Reorder the terms:
-18 + -34w + 4w2 = 18 + -18 + 34w + -34w + -4w2 + 4w2

Combine like terms: 18 + -18 = 0
-18 + -34w + 4w2 = 0 + 34w + -34w + -4w2 + 4w2
-18 + -34w + 4w2 = 34w + -34w + -4w2 + 4w2

Combine like terms: 34w + -34w = 0
-18 + -34w + 4w2 = 0 + -4w2 + 4w2
-18 + -34w + 4w2 = -4w2 + 4w2

Combine like terms: -4w2 + 4w2 = 0
-18 + -34w + 4w2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-9 + -17w + 2w2) = 0

Factor a trinomial.
2((-1 + -2w)(9 + -1w)) = 0

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

Simplifying
-1 + -2w = 0

Solving
-1 + -2w = 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 + -2w = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2w = 0 + 1
-2w = 0 + 1

Combine like terms: 0 + 1 = 1
-2w = 1

Divide each side by '-2'.
w = -0.5

Simplifying
w = -0.5
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 = {-0.5, 9}