(w-2)(w+3)=50

Solution for (w-2)(w+3)=50 equation:

Simplifying
(w + -2)(w + 3) = 50

Reorder the terms:
(-2 + w)(w + 3) = 50

Reorder the terms:
(-2 + w)(3 + w) = 50

Multiply (-2 + w) * (3 + w)
(-2(3 + w) + w(3 + w)) = 50
((3 * -2 + w * -2) + w(3 + w)) = 50
((-6 + -2w) + w(3 + w)) = 50
(-6 + -2w + (3 * w + w * w)) = 50
(-6 + -2w + (3w + w2)) = 50

Combine like terms: -2w + 3w = 1w
(-6 + 1w + w2) = 50

Solving
-6 + 1w + w2 = 50

Solving for variable 'w'.

Reorder the terms:
-6 + -50 + 1w + w2 = 50 + -50

Combine like terms: -6 + -50 = -56
-56 + 1w + w2 = 50 + -50

Combine like terms: 50 + -50 = 0
-56 + 1w + w2 = 0

Factor a trinomial.
(-8 + -1w)(7 + -1w) = 0

Subproblem 1
Set the factor '(-8 + -1w)' equal to zero and attempt to solve:

Simplifying
-8 + -1w = 0

Solving
-8 + -1w = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1w = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1w = 0 + 8
-1w = 0 + 8

Combine like terms: 0 + 8 = 8
-1w = 8

Divide each side by '-1'.
w = -8

Simplifying
w = -8
Subproblem 2
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
Solution
w = {-8, 7}