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

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


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

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

Multiply (2 + -1w) * (7 + 3w)
(2(7 + 3w) + -1w * (7 + 3w)) = 0
((7 * 2 + 3w * 2) + -1w * (7 + 3w)) = 0
((14 + 6w) + -1w * (7 + 3w)) = 0
(14 + 6w + (7 * -1w + 3w * -1w)) = 0
(14 + 6w + (-7w + -3w2)) = 0

Combine like terms: 6w + -7w = -1w
(14 + -1w + -3w2) = 0

Solving
14 + -1w + -3w2 = 0

Solving for variable 'w'.

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


Subproblem 1
Set the factor '(2 + -1w)' equal to zero and attempt to solve:

Simplifying
2 + -1w = 0

Solving
2 + -1w = 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 + -1w = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1w = 0 + -2
-1w = 0 + -2

Combine like terms: 0 + -2 = -2
-1w = -2

Divide each side by '-1'.
w = 2

Simplifying
w = 2

Subproblem 2
Set the factor '(7 + 3w)' equal to zero and attempt to solve:

Simplifying
7 + 3w = 0

Solving
7 + 3w = 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 + 3w = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 3w = 0 + -7
3w = 0 + -7

Combine like terms: 0 + -7 = -7
3w = -7

Divide each side by '3'.
w = -2.333333333

Simplifying
w = -2.333333333
Solution
w = {2, -2.333333333}

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