(w-4)(w+1)=

Solution for (w-4)(w+1)= equation:

Simplifying
(w + -4)(w + 1) = 0

Reorder the terms:
(-4 + w)(w + 1) = 0

Reorder the terms:
(-4 + w)(1 + w) = 0

Multiply (-4 + w) * (1 + w)
(-4(1 + w) + w(1 + w)) = 0
((1 * -4 + w * -4) + w(1 + w)) = 0
((-4 + -4w) + w(1 + w)) = 0
(-4 + -4w + (1 * w + w * w)) = 0
(-4 + -4w + (1w + w2)) = 0

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

Solving
-4 + -3w + w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-1 + -1w)(4 + -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 '(4 + -1w)' equal to zero and attempt to solve:

Simplifying
4 + -1w = 0

Solving
4 + -1w = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1w = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1w = 0 + -4
-1w = 0 + -4

Combine like terms: 0 + -4 = -4
-1w = -4

Divide each side by '-1'.
w = 4

Simplifying
w = 4
Solution
w = {-1, 4}