(3w-7)(w+4)=0

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Solution for (3w-7)(w+4)=0 equation:


Simplifying
(3w + -7)(w + 4) = 0

Reorder the terms:
(-7 + 3w)(w + 4) = 0

Reorder the terms:
(-7 + 3w)(4 + w) = 0

Multiply (-7 + 3w) * (4 + w)
(-7(4 + w) + 3w * (4 + w)) = 0
((4 * -7 + w * -7) + 3w * (4 + w)) = 0
((-28 + -7w) + 3w * (4 + w)) = 0
(-28 + -7w + (4 * 3w + w * 3w)) = 0
(-28 + -7w + (12w + 3w2)) = 0

Combine like terms: -7w + 12w = 5w
(-28 + 5w + 3w2) = 0

Solving
-28 + 5w + 3w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-4 + -1w)(7 + -3w) = 0

Subproblem 1

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

Subproblem 2

Set the factor '(7 + -3w)' equal to zero and attempt to solve: Simplifying 7 + -3w = 0 Solving 7 + -3w = 0 Move all terms containing w to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -3w = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -3w = 0 + -7 -3w = 0 + -7 Combine like terms: 0 + -7 = -7 -3w = -7 Divide each side by '-3'. w = 2.333333333 Simplifying w = 2.333333333

Solution

w = {-4, 2.333333333}

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