4(w-3)(-w+2)=0

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Solution for 4(w-3)(-w+2)=0 equation:


Simplifying
4(w + -3)(-1w + 2) = 0

Reorder the terms:
4(-3 + w)(-1w + 2) = 0

Reorder the terms:
4(-3 + w)(2 + -1w) = 0

Multiply (-3 + w) * (2 + -1w)
4(-3(2 + -1w) + w(2 + -1w)) = 0
4((2 * -3 + -1w * -3) + w(2 + -1w)) = 0
4((-6 + 3w) + w(2 + -1w)) = 0
4(-6 + 3w + (2 * w + -1w * w)) = 0
4(-6 + 3w + (2w + -1w2)) = 0

Combine like terms: 3w + 2w = 5w
4(-6 + 5w + -1w2) = 0
(-6 * 4 + 5w * 4 + -1w2 * 4) = 0
(-24 + 20w + -4w2) = 0

Solving
-24 + 20w + -4w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-6 + 5w + -1w2) = 0

Factor a trinomial.
4((-3 + w)(2 + -1w)) = 0

Ignore the factor 4.

Subproblem 1

Set the factor '(-3 + w)' equal to zero and attempt to solve: Simplifying -3 + w = 0 Solving -3 + w = 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 + w = 0 + 3 Combine like terms: -3 + 3 = 0 0 + w = 0 + 3 w = 0 + 3 Combine like terms: 0 + 3 = 3 w = 3 Simplifying w = 3

Subproblem 2

Set the factor '(2 + -1w)' equal to zero and attempt to solve: Simplifying 2 + -1w = 0 Solving 2 + -1w = 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 + -1w = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1w = 0 + -2 -1w = 0 + -2 Combine like terms: 0 + -2 = -2 -1w = -2 Divide each side by '-1'. w = 2 Simplifying w = 2

Solution

w = {3, 2}

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