2(w+3)(w-1)-(w)(w+3)=84

Solution for 2(w+3)(w-1)-(w)(w+3)=84 equation:

Simplifying
2(w + 3)(w + -1) + -1(w)(w + 3) = 84

Reorder the terms:
2(3 + w)(w + -1) + -1(w)(w + 3) = 84

Reorder the terms:
2(3 + w)(-1 + w) + -1(w)(w + 3) = 84

Multiply (3 + w) * (-1 + w)
2(3(-1 + w) + w(-1 + w)) + -1(w)(w + 3) = 84
2((-1 * 3 + w * 3) + w(-1 + w)) + -1(w)(w + 3) = 84
2((-3 + 3w) + w(-1 + w)) + -1(w)(w + 3) = 84
2(-3 + 3w + (-1 * w + w * w)) + -1(w)(w + 3) = 84
2(-3 + 3w + (-1w + w2)) + -1(w)(w + 3) = 84

Combine like terms: 3w + -1w = 2w
2(-3 + 2w + w2) + -1(w)(w + 3) = 84
(-3 * 2 + 2w * 2 + w2 * 2) + -1(w)(w + 3) = 84
(-6 + 4w + 2w2) + -1(w)(w + 3) = 84

Reorder the terms:
-6 + 4w + 2w2 + -1w(3 + w) = 84
-6 + 4w + 2w2 + (3 * -1w + w * -1w) = 84
-6 + 4w + 2w2 + (-3w + -1w2) = 84

Reorder the terms:
-6 + 4w + -3w + 2w2 + -1w2 = 84

Combine like terms: 4w + -3w = 1w
-6 + 1w + 2w2 + -1w2 = 84

Combine like terms: 2w2 + -1w2 = 1w2
-6 + 1w + 1w2 = 84

Solving
-6 + 1w + 1w2 = 84

Solving for variable 'w'.

Reorder the terms:
-6 + -84 + 1w + 1w2 = 84 + -84

Combine like terms: -6 + -84 = -90
-90 + 1w + 1w2 = 84 + -84

Combine like terms: 84 + -84 = 0
-90 + 1w + 1w2 = 0

Factor a trinomial.
(-10 + -1w)(9 + -1w) = 0

Subproblem 1
Set the factor '(-10 + -1w)' equal to zero and attempt to solve:

Simplifying
-10 + -1w = 0

Solving
-10 + -1w = 0

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

Add '10' to each side of the equation.
-10 + 10 + -1w = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -1w = 0 + 10
-1w = 0 + 10

Combine like terms: 0 + 10 = 10
-1w = 10

Divide each side by '-1'.
w = -10

Simplifying
w = -10
Subproblem 2
Set the factor '(9 + -1w)' equal to zero and attempt to solve:

Simplifying
9 + -1w = 0

Solving
9 + -1w = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1w = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1w = 0 + -9
-1w = 0 + -9

Combine like terms: 0 + -9 = -9
-1w = -9

Divide each side by '-1'.
w = 9

Simplifying
w = 9
Solution
w = {-10, 9}