2w(4w-9)=5

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Solution for 2w(4w-9)=5 equation:


Simplifying
2w(4w + -9) = 5

Reorder the terms:
2w(-9 + 4w) = 5
(-9 * 2w + 4w * 2w) = 5
(-18w + 8w2) = 5

Solving
-18w + 8w2 = 5

Solving for variable 'w'.

Reorder the terms:
-5 + -18w + 8w2 = 5 + -5

Combine like terms: 5 + -5 = 0
-5 + -18w + 8w2 = 0

Factor a trinomial.
(-1 + -4w)(5 + -2w) = 0

Subproblem 1

Set the factor '(-1 + -4w)' equal to zero and attempt to solve: Simplifying -1 + -4w = 0 Solving -1 + -4w = 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 + -4w = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -4w = 0 + 1 -4w = 0 + 1 Combine like terms: 0 + 1 = 1 -4w = 1 Divide each side by '-4'. w = -0.25 Simplifying w = -0.25

Subproblem 2

Set the factor '(5 + -2w)' equal to zero and attempt to solve: Simplifying 5 + -2w = 0 Solving 5 + -2w = 0 Move all terms containing w to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -2w = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2w = 0 + -5 -2w = 0 + -5 Combine like terms: 0 + -5 = -5 -2w = -5 Divide each side by '-2'. w = 2.5 Simplifying w = 2.5

Solution

w = {-0.25, 2.5}

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