(w-7)(w+1)=0

Solution for (w-7)(w+1)=0 equation:

Simplifying
(w + -7)(w + 1) = 0

Reorder the terms:
(-7 + w)(w + 1) = 0

Reorder the terms:
(-7 + w)(1 + w) = 0

Multiply (-7 + w) * (1 + w)
(-7(1 + w) + w(1 + w)) = 0
((1 * -7 + w * -7) + w(1 + w)) = 0
((-7 + -7w) + w(1 + w)) = 0
(-7 + -7w + (1 * w + w * w)) = 0
(-7 + -7w + (1w + w2)) = 0

Combine like terms: -7w + 1w = -6w
(-7 + -6w + w2) = 0

Solving
-7 + -6w + w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-1 + -1w)(7 + -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 '(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 = {-1, 7}