(5-w)(4w-6)=0

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Solution for (5-w)(4w-6)=0 equation:


Simplifying
(5 + -1w)(4w + -6) = 0

Reorder the terms:
(5 + -1w)(-6 + 4w) = 0

Multiply (5 + -1w) * (-6 + 4w)
(5(-6 + 4w) + -1w * (-6 + 4w)) = 0
((-6 * 5 + 4w * 5) + -1w * (-6 + 4w)) = 0
((-30 + 20w) + -1w * (-6 + 4w)) = 0
(-30 + 20w + (-6 * -1w + 4w * -1w)) = 0
(-30 + 20w + (6w + -4w2)) = 0

Combine like terms: 20w + 6w = 26w
(-30 + 26w + -4w2) = 0

Solving
-30 + 26w + -4w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-15 + 13w + -2w2) = 0

Factor a trinomial.
2((-5 + w)(3 + -2w)) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-5 + w)' equal to zero and attempt to solve: Simplifying -5 + w = 0 Solving -5 + w = 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 + w = 0 + 5 Combine like terms: -5 + 5 = 0 0 + w = 0 + 5 w = 0 + 5 Combine like terms: 0 + 5 = 5 w = 5 Simplifying w = 5

Subproblem 2

Set the factor '(3 + -2w)' equal to zero and attempt to solve: Simplifying 3 + -2w = 0 Solving 3 + -2w = 0 Move all terms containing w to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -2w = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2w = 0 + -3 -2w = 0 + -3 Combine like terms: 0 + -3 = -3 -2w = -3 Divide each side by '-2'. w = 1.5 Simplifying w = 1.5

Solution

w = {5, 1.5}

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