(3w-7)(w+8)=0

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Solution for (3w-7)(w+8)=0 equation:


Simplifying
(3w + -7)(w + 8) = 0

Reorder the terms:
(-7 + 3w)(w + 8) = 0

Reorder the terms:
(-7 + 3w)(8 + w) = 0

Multiply (-7 + 3w) * (8 + w)
(-7(8 + w) + 3w * (8 + w)) = 0
((8 * -7 + w * -7) + 3w * (8 + w)) = 0
((-56 + -7w) + 3w * (8 + w)) = 0
(-56 + -7w + (8 * 3w + w * 3w)) = 0
(-56 + -7w + (24w + 3w2)) = 0

Combine like terms: -7w + 24w = 17w
(-56 + 17w + 3w2) = 0

Solving
-56 + 17w + 3w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-8 + -1w)(7 + -3w) = 0

Subproblem 1

Set the factor '(-8 + -1w)' equal to zero and attempt to solve: Simplifying -8 + -1w = 0 Solving -8 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + -1w = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -1w = 0 + 8 -1w = 0 + 8 Combine like terms: 0 + 8 = 8 -1w = 8 Divide each side by '-1'. w = -8 Simplifying w = -8

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 = {-8, 2.333333333}

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