(3bc^2d^3)(4b^2-c^2)(-5d^4)=

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Solution for (3bc^2d^3)(4b^2-c^2)(-5d^4)= equation: 


Simplifying
(3bc2d3)(4b2 + -1c2)(-5d4) = 0

Remove parenthesis around (3bc2d3)
3bc2d3(4b2 + -1c2)(-5d4) = 0

Remove parenthesis around (-5d4)
3bc2d3(4b2 + -1c2) * -5d4 = 0

Reorder the terms for easier multiplication:
3 * -5bc2d3 * d4(4b2 + -1c2) = 0

Multiply 3 * -5
-15bc2d3 * d4(4b2 + -1c2) = 0

Multiply bc2d3 * d4
-15bc2d7(4b2 + -1c2) = 0
(4b2 * -15bc2d7 + -1c2 * -15bc2d7) = 0

Reorder the terms:
(15bc4d7 + -60b3c2d7) = 0
(15bc4d7 + -60b3c2d7) = 0

Solving
15bc4d7 + -60b3c2d7 = 0

Solving for variable 'b'.

Factor out the Greatest Common Factor (GCF), '15bc2d7'.
15bc2d7(c2 + -4b2) = 0

Factor a difference between two squares.
15bc2d7((c + 2b)(c + -2b)) = 0

Ignore the factor 15.

Subproblem 1
Set the factor 'bc2d7' equal to zero and attempt to solve:

Simplifying
bc2d7 = 0

Solving
bc2d7 = 0

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

Simplifying
bc2d7 = 0

The solution to this equation could not be determined.

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

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

Simplifying
c + 2b = 0

Reorder the terms:
2b + c = 0

Solving
2b + c = 0

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

Add '-1c' to each side of the equation.
2b + c + -1c = 0 + -1c

Combine like terms: c + -1c = 0
2b + 0 = 0 + -1c
2b = 0 + -1c
Remove the zero:
2b = -1c

Divide each side by '2'.
b = -0.5c

Simplifying
b = -0.5c

Subproblem 3
Set the factor '(c + -2b)' equal to zero and attempt to solve:

Simplifying
c + -2b = 0

Reorder the terms:
-2b + c = 0

Solving
-2b + c = 0

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

Add '-1c' to each side of the equation.
-2b + c + -1c = 0 + -1c

Combine like terms: c + -1c = 0
-2b + 0 = 0 + -1c
-2b = 0 + -1c
Remove the zero:
-2b = -1c

Divide each side by '-2'.
b = 0.5c

Simplifying
b = 0.5c
Solution
b = {-0.5c, 0.5c}

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