(w-3)(w+1)=

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

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

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

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

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

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

Solving
-3 + -2w + w2 = 0

Solving for variable 'w'.

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

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

Simplifying
-1 + -1w = 0

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

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

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

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

Simplifying
w = -1
Subproblem 2
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
Solution
w = {-1, 3}