2(w+7)(w-3)=w^2+7w+68

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Solution for 2(w+7)(w-3)=w^2+7w+68 equation: 


Simplifying
2(w + 7)(w + -3) = w2 + 7w + 68

Reorder the terms:
2(7 + w)(w + -3) = w2 + 7w + 68

Reorder the terms:
2(7 + w)(-3 + w) = w2 + 7w + 68

Multiply (7 + w) * (-3 + w)
2(7(-3 + w) + w(-3 + w)) = w2 + 7w + 68
2((-3 * 7 + w * 7) + w(-3 + w)) = w2 + 7w + 68
2((-21 + 7w) + w(-3 + w)) = w2 + 7w + 68
2(-21 + 7w + (-3 * w + w * w)) = w2 + 7w + 68
2(-21 + 7w + (-3w + w2)) = w2 + 7w + 68

Combine like terms: 7w + -3w = 4w
2(-21 + 4w + w2) = w2 + 7w + 68
(-21 * 2 + 4w * 2 + w2 * 2) = w2 + 7w + 68
(-42 + 8w + 2w2) = w2 + 7w + 68

Reorder the terms:
-42 + 8w + 2w2 = 68 + 7w + w2

Solving
-42 + 8w + 2w2 = 68 + 7w + w2

Solving for variable 'w'.

Reorder the terms:
-42 + -68 + 8w + -7w + 2w2 + -1w2 = 68 + 7w + w2 + -68 + -7w + -1w2

Combine like terms: -42 + -68 = -110
-110 + 8w + -7w + 2w2 + -1w2 = 68 + 7w + w2 + -68 + -7w + -1w2

Combine like terms: 8w + -7w = 1w
-110 + 1w + 2w2 + -1w2 = 68 + 7w + w2 + -68 + -7w + -1w2

Combine like terms: 2w2 + -1w2 = 1w2
-110 + 1w + 1w2 = 68 + 7w + w2 + -68 + -7w + -1w2

Reorder the terms:
-110 + 1w + 1w2 = 68 + -68 + 7w + -7w + w2 + -1w2

Combine like terms: 68 + -68 = 0
-110 + 1w + 1w2 = 0 + 7w + -7w + w2 + -1w2
-110 + 1w + 1w2 = 7w + -7w + w2 + -1w2

Combine like terms: 7w + -7w = 0
-110 + 1w + 1w2 = 0 + w2 + -1w2
-110 + 1w + 1w2 = w2 + -1w2

Combine like terms: w2 + -1w2 = 0
-110 + 1w + 1w2 = 0

Factor a trinomial.
(-11 + -1w)(10 + -1w) = 0


Subproblem 1
Set the factor '(-11 + -1w)' equal to zero and attempt to solve:

Simplifying
-11 + -1w = 0

Solving
-11 + -1w = 0

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

Add '11' to each side of the equation.
-11 + 11 + -1w = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -1w = 0 + 11
-1w = 0 + 11

Combine like terms: 0 + 11 = 11
-1w = 11

Divide each side by '-1'.
w = -11

Simplifying
w = -11

Subproblem 2
Set the factor '(10 + -1w)' equal to zero and attempt to solve:

Simplifying
10 + -1w = 0

Solving
10 + -1w = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1w = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1w = 0 + -10
-1w = 0 + -10

Combine like terms: 0 + -10 = -10
-1w = -10

Divide each side by '-1'.
w = 10

Simplifying
w = 10
Solution
w = {-11, 10}

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