(4w+6)(7-w)=0

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Solution for (4w+6)(7-w)=0 equation:


Simplifying
(4w + 6)(7 + -1w) = 0

Reorder the terms:
(6 + 4w)(7 + -1w) = 0

Multiply (6 + 4w) * (7 + -1w)
(6(7 + -1w) + 4w * (7 + -1w)) = 0
((7 * 6 + -1w * 6) + 4w * (7 + -1w)) = 0
((42 + -6w) + 4w * (7 + -1w)) = 0
(42 + -6w + (7 * 4w + -1w * 4w)) = 0
(42 + -6w + (28w + -4w2)) = 0

Combine like terms: -6w + 28w = 22w
(42 + 22w + -4w2) = 0

Solving
42 + 22w + -4w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '2'.
2(21 + 11w + -2w2) = 0

Factor a trinomial.
2((7 + -1w)(3 + 2w)) = 0

Ignore the factor 2.

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 '(3 + 2w)' equal to zero and attempt to solve: Simplifying 3 + 2w = 0 Solving 3 + 2w = 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 + 2w = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2w = 0 + -3 2w = 0 + -3 Combine like terms: 0 + -3 = -3 2w = -3 Divide each side by '2'. w = -1.5 Simplifying w = -1.5

Solution

w = {7, -1.5}

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