(2w+3)(7-w)=0

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Solution for (2w+3)(7-w)=0 equation: 


Simplifying
(2w + 3)(7 + -1w) = 0

Reorder the terms:
(3 + 2w)(7 + -1w) = 0

Multiply (3 + 2w) * (7 + -1w)
(3(7 + -1w) + 2w * (7 + -1w)) = 0
((7 * 3 + -1w * 3) + 2w * (7 + -1w)) = 0
((21 + -3w) + 2w * (7 + -1w)) = 0
(21 + -3w + (7 * 2w + -1w * 2w)) = 0
(21 + -3w + (14w + -2w2)) = 0

Combine like terms: -3w + 14w = 11w
(21 + 11w + -2w2) = 0

Solving
21 + 11w + -2w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(7 + -1w)(3 + 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 '(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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