2w(6w+8)=2w(4w+24)

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Solution for 2w(6w+8)=2w(4w+24) equation: 


Simplifying
2w(6w + 8) = 2w(4w + 24)

Reorder the terms:
2w(8 + 6w) = 2w(4w + 24)
(8 * 2w + 6w * 2w) = 2w(4w + 24)
(16w + 12w2) = 2w(4w + 24)

Reorder the terms:
16w + 12w2 = 2w(24 + 4w)
16w + 12w2 = (24 * 2w + 4w * 2w)
16w + 12w2 = (48w + 8w2)

Solving
16w + 12w2 = 48w + 8w2

Solving for variable 'w'.

Reorder the terms:
16w + -48w + 12w2 + -8w2 = 48w + 8w2 + -48w + -8w2

Combine like terms: 16w + -48w = -32w
-32w + 12w2 + -8w2 = 48w + 8w2 + -48w + -8w2

Combine like terms: 12w2 + -8w2 = 4w2
-32w + 4w2 = 48w + 8w2 + -48w + -8w2

Reorder the terms:
-32w + 4w2 = 48w + -48w + 8w2 + -8w2

Combine like terms: 48w + -48w = 0
-32w + 4w2 = 0 + 8w2 + -8w2
-32w + 4w2 = 8w2 + -8w2

Combine like terms: 8w2 + -8w2 = 0
-32w + 4w2 = 0

Factor out the Greatest Common Factor (GCF), '4w'.
4w(-8 + w) = 0

Ignore the factor 4.

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 '(-8 + w)' equal to zero and attempt to solve:

Simplifying
-8 + w = 0

Solving
-8 + w = 0

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

Add '8' to each side of the equation.
-8 + 8 + w = 0 + 8

Combine like terms: -8 + 8 = 0
0 + w = 0 + 8
w = 0 + 8

Combine like terms: 0 + 8 = 8
w = 8

Simplifying
w = 8
Solution
w = {0, 8}

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