=(w+2)(w-7)

Solution for =(w+2)(w-7) equation:

Simplifying
0 = (w + 2)(w + -7)

Reorder the terms:
0 = (2 + w)(w + -7)

Reorder the terms:
0 = (2 + w)(-7 + w)

Multiply (2 + w) * (-7 + w)
0 = (2(-7 + w) + w(-7 + w))
0 = ((-7 * 2 + w * 2) + w(-7 + w))
0 = ((-14 + 2w) + w(-7 + w))
0 = (-14 + 2w + (-7 * w + w * w))
0 = (-14 + 2w + (-7w + w2))

Combine like terms: 2w + -7w = -5w
0 = (-14 + -5w + w2)

Solving
0 = -14 + -5w + w2

Solving for variable 'w'.

Combine like terms: 0 + 14 = 14
14 + 5w + -1w2 = -14 + -5w + w2 + 14 + 5w + -1w2

Reorder the terms:
14 + 5w + -1w2 = -14 + 14 + -5w + 5w + w2 + -1w2

Combine like terms: -14 + 14 = 0
14 + 5w + -1w2 = 0 + -5w + 5w + w2 + -1w2
14 + 5w + -1w2 = -5w + 5w + w2 + -1w2

Combine like terms: -5w + 5w = 0
14 + 5w + -1w2 = 0 + w2 + -1w2
14 + 5w + -1w2 = w2 + -1w2

Combine like terms: w2 + -1w2 = 0
14 + 5w + -1w2 = 0

Factor a trinomial.
(7 + -1w)(2 + w) = 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 '(2 + w)' equal to zero and attempt to solve:

Simplifying
2 + w = 0

Solving
2 + w = 0

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

Add '-2' to each side of the equation.
2 + -2 + w = 0 + -2

Combine like terms: 2 + -2 = 0
0 + w = 0 + -2
w = 0 + -2

Combine like terms: 0 + -2 = -2
w = -2

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