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

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


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

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

Multiply (-6 + 4w) * (4 + -1w)
(-6(4 + -1w) + 4w * (4 + -1w)) = 0
((4 * -6 + -1w * -6) + 4w * (4 + -1w)) = 0
((-24 + 6w) + 4w * (4 + -1w)) = 0
(-24 + 6w + (4 * 4w + -1w * 4w)) = 0
(-24 + 6w + (16w + -4w2)) = 0

Combine like terms: 6w + 16w = 22w
(-24 + 22w + -4w2) = 0

Solving
-24 + 22w + -4w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-12 + 11w + -2w2) = 0

Factor a trinomial.
2((-4 + w)(3 + -2w)) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-4 + w)' equal to zero and attempt to solve: Simplifying -4 + w = 0 Solving -4 + w = 0 Move all terms containing w to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + w = 0 + 4 Combine like terms: -4 + 4 = 0 0 + w = 0 + 4 w = 0 + 4 Combine like terms: 0 + 4 = 4 w = 4 Simplifying w = 4

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 = {4, 1.5}

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