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

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


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

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

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

Combine like terms: -2w + 21w = 19w
(14 + 19w + -3w2) = 0

Solving
14 + 19w + -3w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(7 + -1w)(2 + 3w) = 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 '(2 + 3w)' equal to zero and attempt to solve:

Simplifying
2 + 3w = 0

Solving
2 + 3w = 0

Move all terms containing w to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + 3w = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3w = 0 + -2
3w = 0 + -2

Combine like terms: 0 + -2 = -2
3w = -2

Divide each side by '3'.
w = -0.6666666667

Simplifying
w = -0.6666666667
Solution
w = {7, -0.6666666667}

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