(4w+1)(7-w)=0

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Solution for (4w+1)(7-w)=0 equation:


Simplifying
(4w + 1)(7 + -1w) = 0

Reorder the terms:
(1 + 4w)(7 + -1w) = 0

Multiply (1 + 4w) * (7 + -1w)
(1(7 + -1w) + 4w * (7 + -1w)) = 0
((7 * 1 + -1w * 1) + 4w * (7 + -1w)) = 0
((7 + -1w) + 4w * (7 + -1w)) = 0
(7 + -1w + (7 * 4w + -1w * 4w)) = 0
(7 + -1w + (28w + -4w2)) = 0

Combine like terms: -1w + 28w = 27w
(7 + 27w + -4w2) = 0

Solving
7 + 27w + -4w2 = 0

Solving for variable 'w'.

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

Subproblem 1

Set the factor '(7 + -1w)' equal to zero and attempt to solve: Simplifying 7 + -1w = 0 Solving 7 + -1w = 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 + -1w = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1w = 0 + -7 -1w = 0 + -7 Combine like terms: 0 + -7 = -7 -1w = -7 Divide each side by '-1'. w = 7 Simplifying w = 7

Subproblem 2

Set the factor '(1 + 4w)' equal to zero and attempt to solve: Simplifying 1 + 4w = 0 Solving 1 + 4w = 0 Move all terms containing w to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 4w = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 4w = 0 + -1 4w = 0 + -1 Combine like terms: 0 + -1 = -1 4w = -1 Divide each side by '4'. w = -0.25 Simplifying w = -0.25

Solution

w = {7, -0.25}

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