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

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

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

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

Multiply (3 + w) * (-7 + 3w)
(3(-7 + 3w) + w(-7 + 3w)) = 0
((-7 * 3 + 3w * 3) + w(-7 + 3w)) = 0
((-21 + 9w) + w(-7 + 3w)) = 0
(-21 + 9w + (-7 * w + 3w * w)) = 0
(-21 + 9w + (-7w + 3w2)) = 0

Combine like terms: 9w + -7w = 2w
(-21 + 2w + 3w2) = 0

Solving
-21 + 2w + 3w2 = 0

Solving for variable 'w'.

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

Subproblem 1
Set the factor '(-3 + -1w)' equal to zero and attempt to solve:

Simplifying
-3 + -1w = 0

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

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

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

Divide each side by '-1'.
w = -3

Simplifying
w = -3
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 = {-3, 2.333333333}