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

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

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

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

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

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

Solving
-18 + 34w + 4w2 = 0

Solving for variable 'w'.

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

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

Ignore the factor 2.
Subproblem 1
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
Subproblem 2
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
Solution
w = {-9, 0.5}