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

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


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

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

Multiply (-7 + 4w) * (4 + w)
(-7(4 + w) + 4w * (4 + w)) = 0
((4 * -7 + w * -7) + 4w * (4 + w)) = 0
((-28 + -7w) + 4w * (4 + w)) = 0
(-28 + -7w + (4 * 4w + w * 4w)) = 0
(-28 + -7w + (16w + 4w2)) = 0

Combine like terms: -7w + 16w = 9w
(-28 + 9w + 4w2) = 0

Solving
-28 + 9w + 4w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-4 + -1w)(7 + -4w) = 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 + -4w)' equal to zero and attempt to solve: Simplifying 7 + -4w = 0 Solving 7 + -4w = 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 + -4w = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -4w = 0 + -7 -4w = 0 + -7 Combine like terms: 0 + -7 = -7 -4w = -7 Divide each side by '-4'. w = 1.75 Simplifying w = 1.75

Solution

w = {-4, 1.75}

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