4w(2w+8)-7(2w+8)=0

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Solution for 4w(2w+8)-7(2w+8)=0 equation: 


Simplifying
4w(2w + 8) + -7(2w + 8) = 0

Reorder the terms:
4w(8 + 2w) + -7(2w + 8) = 0
(8 * 4w + 2w * 4w) + -7(2w + 8) = 0
(32w + 8w2) + -7(2w + 8) = 0

Reorder the terms:
32w + 8w2 + -7(8 + 2w) = 0
32w + 8w2 + (8 * -7 + 2w * -7) = 0
32w + 8w2 + (-56 + -14w) = 0

Reorder the terms:
-56 + 32w + -14w + 8w2 = 0

Combine like terms: 32w + -14w = 18w
-56 + 18w + 8w2 = 0

Solving
-56 + 18w + 8w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-28 + 9w + 4w2) = 0

Factor a trinomial.
2((-4 + -1w)(7 + -4w)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-4 + -1w)' equal to zero and attempt to solve:

Simplifying
-4 + -1w = 0

Solving
-4 + -1w = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1w = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1w = 0 + 4
-1w = 0 + 4

Combine like terms: 0 + 4 = 4
-1w = 4

Divide each side by '-1'.
w = -4

Simplifying
w = -4

Subproblem 2
Set the factor '(7 + -4w)' equal to zero and attempt to solve:

Simplifying
7 + -4w = 0

Solving
7 + -4w = 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 + -4w = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -4w = 0 + -7
-4w = 0 + -7

Combine like terms: 0 + -7 = -7
-4w = -7

Divide each side by '-4'.
w = 1.75

Simplifying
w = 1.75
Solution
w = {-4, 1.75}

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