(3+4x)*4w*(3+4x)*4w=76

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Solution for (3+4x)*4w*(3+4x)*4w=76 equation: 


Simplifying
(3 + 4x) * 4w(3 + 4x) * 4w = 76

Reorder the terms for easier multiplication:
4 * 4w * w(3 + 4x)(3 + 4x) = 76

Multiply 4 * 4
16w * w(3 + 4x)(3 + 4x) = 76

Multiply w * w
16w2(3 + 4x)(3 + 4x) = 76

Multiply (3 + 4x) * (3 + 4x)
16w2(3(3 + 4x) + 4x * (3 + 4x)) = 76
16w2((3 * 3 + 4x * 3) + 4x * (3 + 4x)) = 76
16w2((9 + 12x) + 4x * (3 + 4x)) = 76
16w2(9 + 12x + (3 * 4x + 4x * 4x)) = 76
16w2(9 + 12x + (12x + 16x2)) = 76

Combine like terms: 12x + 12x = 24x
16w2(9 + 24x + 16x2) = 76
(9 * 16w2 + 24x * 16w2 + 16x2 * 16w2) = 76
(144w2 + 384w2x + 256w2x2) = 76

Solving
144w2 + 384w2x + 256w2x2 = 76

Solving for variable 'w'.

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

Reorder the terms:
-76 + 144w2 + 384w2x + 256w2x2 = 76 + -76

Combine like terms: 76 + -76 = 0
-76 + 144w2 + 384w2x + 256w2x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-19 + 36w2 + 96w2x + 64w2x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-19 + 36w2 + 96w2x + 64w2x2)' equal to zero and attempt to solve:

Simplifying
-19 + 36w2 + 96w2x + 64w2x2 = 0

Solving
-19 + 36w2 + 96w2x + 64w2x2 = 0

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

Add '19' to each side of the equation.
-19 + 36w2 + 96w2x + 19 + 64w2x2 = 0 + 19

Reorder the terms:
-19 + 19 + 36w2 + 96w2x + 64w2x2 = 0 + 19

Combine like terms: -19 + 19 = 0
0 + 36w2 + 96w2x + 64w2x2 = 0 + 19
36w2 + 96w2x + 64w2x2 = 0 + 19

Combine like terms: 0 + 19 = 19
36w2 + 96w2x + 64w2x2 = 19

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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