(w-3)(w+7)=

Solution for (w-3)(w+7)= equation:

Simplifying
(w + -3)(w + 7) = 0

Reorder the terms:
(-3 + w)(w + 7) = 0

Reorder the terms:
(-3 + w)(7 + w) = 0

Multiply (-3 + w) * (7 + w)
(-3(7 + w) + w(7 + w)) = 0
((7 * -3 + w * -3) + w(7 + w)) = 0
((-21 + -3w) + w(7 + w)) = 0
(-21 + -3w + (7 * w + w * w)) = 0
(-21 + -3w + (7w + w2)) = 0

Combine like terms: -3w + 7w = 4w
(-21 + 4w + w2) = 0

Solving
-21 + 4w + w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-7 + -1w)(3 + -1w) = 0

Subproblem 1
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
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 = {-7, 3}