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

Solution for 2(w+3)(w-1)-(w)(w+3)=0 equation:

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

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

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

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

Combine like terms: 3w + -1w = 2w
2(-3 + 2w + w2) + -1(w)(w + 3) = 0
(-3 * 2 + 2w * 2 + w2 * 2) + -1(w)(w + 3) = 0
(-6 + 4w + 2w2) + -1(w)(w + 3) = 0

Reorder the terms:
-6 + 4w + 2w2 + -1w(3 + w) = 0
-6 + 4w + 2w2 + (3 * -1w + w * -1w) = 0
-6 + 4w + 2w2 + (-3w + -1w2) = 0

Reorder the terms:
-6 + 4w + -3w + 2w2 + -1w2 = 0

Combine like terms: 4w + -3w = 1w
-6 + 1w + 2w2 + -1w2 = 0

Combine like terms: 2w2 + -1w2 = 1w2
-6 + 1w + 1w2 = 0

Solving
-6 + 1w + 1w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-3 + -1w)(2 + -1w) = 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 '(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
Solution
w = {-3, 2}