2(W+7)(W-3)=W^2+7W+168

Solution for 2(W+7)(W-3)=W^2+7W+168 equation:

Simplifying
2(W + 7)(W + -3) = W2 + 7W + 168

Reorder the terms:
2(7 + W)(W + -3) = W2 + 7W + 168

Reorder the terms:
2(7 + W)(-3 + W) = W2 + 7W + 168

Multiply (7 + W) * (-3 + W)
2(7(-3 + W) + W(-3 + W)) = W2 + 7W + 168
2((-3 * 7 + W * 7) + W(-3 + W)) = W2 + 7W + 168
2((-21 + 7W) + W(-3 + W)) = W2 + 7W + 168
2(-21 + 7W + (-3 * W + W * W)) = W2 + 7W + 168
2(-21 + 7W + (-3W + W2)) = W2 + 7W + 168

Combine like terms: 7W + -3W = 4W
2(-21 + 4W + W2) = W2 + 7W + 168
(-21 * 2 + 4W * 2 + W2 * 2) = W2 + 7W + 168
(-42 + 8W + 2W2) = W2 + 7W + 168

Reorder the terms:
-42 + 8W + 2W2 = 168 + 7W + W2

Solving
-42 + 8W + 2W2 = 168 + 7W + W2

Solving for variable 'W'.

Reorder the terms:
-42 + -168 + 8W + -7W + 2W2 + -1W2 = 168 + 7W + W2 + -168 + -7W + -1W2

Combine like terms: -42 + -168 = -210
-210 + 8W + -7W + 2W2 + -1W2 = 168 + 7W + W2 + -168 + -7W + -1W2

Combine like terms: 8W + -7W = 1W
-210 + 1W + 2W2 + -1W2 = 168 + 7W + W2 + -168 + -7W + -1W2

Combine like terms: 2W2 + -1W2 = 1W2
-210 + 1W + 1W2 = 168 + 7W + W2 + -168 + -7W + -1W2

Reorder the terms:
-210 + 1W + 1W2 = 168 + -168 + 7W + -7W + W2 + -1W2

Combine like terms: 168 + -168 = 0
-210 + 1W + 1W2 = 0 + 7W + -7W + W2 + -1W2
-210 + 1W + 1W2 = 7W + -7W + W2 + -1W2

Combine like terms: 7W + -7W = 0
-210 + 1W + 1W2 = 0 + W2 + -1W2
-210 + 1W + 1W2 = W2 + -1W2

Combine like terms: W2 + -1W2 = 0
-210 + 1W + 1W2 = 0

Factor a trinomial.
(-15 + -1W)(14 + -1W) = 0

Subproblem 1
Set the factor '(-15 + -1W)' equal to zero and attempt to solve:

Simplifying
-15 + -1W = 0

Solving
-15 + -1W = 0

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

Add '15' to each side of the equation.
-15 + 15 + -1W = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -1W = 0 + 15
-1W = 0 + 15

Combine like terms: 0 + 15 = 15
-1W = 15

Divide each side by '-1'.
W = -15

Simplifying
W = -15
Subproblem 2
Set the factor '(14 + -1W)' equal to zero and attempt to solve:

Simplifying
14 + -1W = 0

Solving
14 + -1W = 0

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

Add '-14' to each side of the equation.
14 + -14 + -1W = 0 + -14

Combine like terms: 14 + -14 = 0
0 + -1W = 0 + -14
-1W = 0 + -14

Combine like terms: 0 + -14 = -14
-1W = -14

Divide each side by '-1'.
W = 14

Simplifying
W = 14
Solution
W = {-15, 14}