2a(-4b+8c)-5a(6b-c)=

Solution for 2a(-4b+8c)-5a(6b-c)= equation:

Simplifying
2a(-4b + 8c) + -5a(6b + -1c) = 0
(-4b * 2a + 8c * 2a) + -5a(6b + -1c) = 0
(-8ab + 16ac) + -5a(6b + -1c) = 0
-8ab + 16ac + (6b * -5a + -1c * -5a) = 0
-8ab + 16ac + (-30ab + 5ac) = 0

Reorder the terms:
-8ab + -30ab + 16ac + 5ac = 0

Combine like terms: -8ab + -30ab = -38ab
-38ab + 16ac + 5ac = 0

Combine like terms: 16ac + 5ac = 21ac
-38ab + 21ac = 0

Solving
-38ab + 21ac = 0

Solving for variable 'a'.

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

Factor out the Greatest Common Factor (GCF), 'a'.
a(-38b + 21c) = 0

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

Simplifying
a = 0

Solving
a = 0

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

Simplifying
a = 0
Subproblem 2
Set the factor '(-38b + 21c)' equal to zero and attempt to solve:

Simplifying
-38b + 21c = 0

Solving
-38b + 21c = 0

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

Add '38b' to each side of the equation.
-38b + 38b + 21c = 0 + 38b

Combine like terms: -38b + 38b = 0
0 + 21c = 0 + 38b
21c = 0 + 38b
Remove the zero:
21c = 38b

Add '-21c' to each side of the equation.
21c + -21c = 38b + -21c

Combine like terms: 21c + -21c = 0
0 = 38b + -21c

Simplifying
0 = 38b + -21c

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
a = {0}