=2ab(3a-4c+5d)

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Solution for =2ab(3a-4c+5d) equation: 


Simplifying
0 = 2ab(3a + -4c + 5d)
0 = (3a * 2ab + -4c * 2ab + 5d * 2ab)

Reorder the terms:
0 = (-8abc + 10abd + 6a2b)
0 = (-8abc + 10abd + 6a2b)

Solving
0 = -8abc + 10abd + 6a2b

Solving for variable 'a'.
Remove the zero:
8abc + -10abd + -6a2b = -8abc + 10abd + 6a2b + 8abc + -10abd + -6a2b

Reorder the terms:
8abc + -10abd + -6a2b = -8abc + 8abc + 10abd + -10abd + 6a2b + -6a2b

Combine like terms: -8abc + 8abc = 0
8abc + -10abd + -6a2b = 0 + 10abd + -10abd + 6a2b + -6a2b
8abc + -10abd + -6a2b = 10abd + -10abd + 6a2b + -6a2b

Combine like terms: 10abd + -10abd = 0
8abc + -10abd + -6a2b = 0 + 6a2b + -6a2b
8abc + -10abd + -6a2b = 6a2b + -6a2b

Combine like terms: 6a2b + -6a2b = 0
8abc + -10abd + -6a2b = 0

Factor out the Greatest Common Factor (GCF), '2ab'.
2ab(4c + -5d + -3a) = 0

Ignore the factor 2.

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

Simplifying
ab = 0

Solving
ab = 0

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

Simplifying
ab = 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 '(4c + -5d + -3a)' equal to zero and attempt to solve:

Simplifying
4c + -5d + -3a = 0

Reorder the terms:
-3a + 4c + -5d = 0

Solving
-3a + 4c + -5d = 0

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

Add '-4c' to each side of the equation.
-3a + 4c + -4c + -5d = 0 + -4c

Combine like terms: 4c + -4c = 0
-3a + 0 + -5d = 0 + -4c
-3a + -5d = 0 + -4c
Remove the zero:
-3a + -5d = -4c

Add '5d' to each side of the equation.
-3a + -5d + 5d = -4c + 5d

Combine like terms: -5d + 5d = 0
-3a + 0 = -4c + 5d
-3a = -4c + 5d

Divide each side by '-3'.
a = 1.333333333c + -1.666666667d

Simplifying
a = 1.333333333c + -1.666666667d
Solution
a = {1.333333333c + -1.666666667d}

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