(2w+27)(2w+8)-(8*27)=0

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Solution for (2w+27)(2w+8)-(8*27)=0 equation: 


Simplifying
(2w + 27)(2w + 8) + -1(8 * 27) = 0

Reorder the terms:
(27 + 2w)(2w + 8) + -1(8 * 27) = 0

Reorder the terms:
(27 + 2w)(8 + 2w) + -1(8 * 27) = 0

Multiply (27 + 2w) * (8 + 2w)
(27(8 + 2w) + 2w * (8 + 2w)) + -1(8 * 27) = 0
((8 * 27 + 2w * 27) + 2w * (8 + 2w)) + -1(8 * 27) = 0
((216 + 54w) + 2w * (8 + 2w)) + -1(8 * 27) = 0
(216 + 54w + (8 * 2w + 2w * 2w)) + -1(8 * 27) = 0
(216 + 54w + (16w + 4w2)) + -1(8 * 27) = 0

Combine like terms: 54w + 16w = 70w
(216 + 70w + 4w2) + -1(8 * 27) = 0

Multiply 8 * 27
216 + 70w + 4w2 + -1(216) = 0

Multiply -1 * 216
216 + 70w + 4w2 + -216 = 0

Reorder the terms:
216 + -216 + 70w + 4w2 = 0

Combine like terms: 216 + -216 = 0
0 + 70w + 4w2 = 0
70w + 4w2 = 0

Solving
70w + 4w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '2w'.
2w(35 + 2w) = 0

Ignore the factor 2.

Subproblem 1
Set the factor 'w' equal to zero and attempt to solve:

Simplifying
w = 0

Solving
w = 0

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

Simplifying
w = 0

Subproblem 2
Set the factor '(35 + 2w)' equal to zero and attempt to solve:

Simplifying
35 + 2w = 0

Solving
35 + 2w = 0

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

Add '-35' to each side of the equation.
35 + -35 + 2w = 0 + -35

Combine like terms: 35 + -35 = 0
0 + 2w = 0 + -35
2w = 0 + -35

Combine like terms: 0 + -35 = -35
2w = -35

Divide each side by '2'.
w = -17.5

Simplifying
w = -17.5
Solution
w = {0, -17.5}

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