(2w+9)(7-w)=0

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Solution for (2w+9)(7-w)=0 equation:


Simplifying
(2w + 9)(7 + -1w) = 0

Reorder the terms:
(9 + 2w)(7 + -1w) = 0

Multiply (9 + 2w) * (7 + -1w)
(9(7 + -1w) + 2w * (7 + -1w)) = 0
((7 * 9 + -1w * 9) + 2w * (7 + -1w)) = 0
((63 + -9w) + 2w * (7 + -1w)) = 0
(63 + -9w + (7 * 2w + -1w * 2w)) = 0
(63 + -9w + (14w + -2w2)) = 0

Combine like terms: -9w + 14w = 5w
(63 + 5w + -2w2) = 0

Solving
63 + 5w + -2w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(7 + -1w)(9 + 2w) = 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 '(9 + 2w)' equal to zero and attempt to solve: Simplifying 9 + 2w = 0 Solving 9 + 2w = 0 Move all terms containing w to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + 2w = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 2w = 0 + -9 2w = 0 + -9 Combine like terms: 0 + -9 = -9 2w = -9 Divide each side by '2'. w = -4.5 Simplifying w = -4.5

Solution

w = {7, -4.5}

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