2w(9w-2)(2w-1)=0

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Solution for 2w(9w-2)(2w-1)=0 equation: 


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

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

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

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

Combine like terms: -4w + -9w = -13w
2w(2 + -13w + 18w2) = 0
(2 * 2w + -13w * 2w + 18w2 * 2w) = 0
(4w + -26w2 + 36w3) = 0

Solving
4w + -26w2 + 36w3 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '2w'.
2w(2 + -13w + 18w2) = 0

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

Ignore the factor 2.

Subproblem 1
Set the factor 'w' equal to zero and attempt to solve:

Simplifying
w = 0

Solving
w = 0

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

Simplifying
w = 0

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

Simplifying
2 + -9w = 0

Solving
2 + -9w = 0

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

Add '-2' to each side of the equation.
2 + -2 + -9w = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -9w = 0 + -2
-9w = 0 + -2

Combine like terms: 0 + -2 = -2
-9w = -2

Divide each side by '-9'.
w = 0.2222222222

Simplifying
w = 0.2222222222

Subproblem 3
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 = {0, 0.2222222222, 0.5}

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