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

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Solution for (3w-1)(w+7)=0 equation: 


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

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

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

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

Combine like terms: -1w + 21w = 20w
(-7 + 20w + 3w2) = 0

Solving
-7 + 20w + 3w2 = 0

Solving for variable 'w'.

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

Simplifying
1 + -3w = 0

Solving
1 + -3w = 0

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

Add '-1' to each side of the equation.
1 + -1 + -3w = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3w = 0 + -1
-3w = 0 + -1

Combine like terms: 0 + -1 = -1
-3w = -1

Divide each side by '-3'.
w = 0.3333333333

Simplifying
w = 0.3333333333
Solution
w = {-7, 0.3333333333}

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