=-6a(a-b+4c)

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


Simplifying
0 = -6a(a + -1b + 4c)
0 = (a * -6a + -1b * -6a + 4c * -6a)

Reorder the terms:
0 = (6ab + -24ac + -6a2)
0 = (6ab + -24ac + -6a2)

Solving
0 = 6ab + -24ac + -6a2

Solving for variable 'a'.
Remove the zero:
-6ab + 24ac + 6a2 = 6ab + -24ac + -6a2 + -6ab + 24ac + 6a2

Reorder the terms:
-6ab + 24ac + 6a2 = 6ab + -6ab + -24ac + 24ac + -6a2 + 6a2

Combine like terms: 6ab + -6ab = 0
-6ab + 24ac + 6a2 = 0 + -24ac + 24ac + -6a2 + 6a2
-6ab + 24ac + 6a2 = -24ac + 24ac + -6a2 + 6a2

Combine like terms: -24ac + 24ac = 0
-6ab + 24ac + 6a2 = 0 + -6a2 + 6a2
-6ab + 24ac + 6a2 = -6a2 + 6a2

Combine like terms: -6a2 + 6a2 = 0
-6ab + 24ac + 6a2 = 0

Factor out the Greatest Common Factor (GCF), '6a'.
6a(-1b + 4c + a) = 0

Ignore the factor 6.

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 '(-1b + 4c + a)' equal to zero and attempt to solve:

Simplifying
-1b + 4c + a = 0

Reorder the terms:
a + -1b + 4c = 0

Solving
a + -1b + 4c = 0

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

Add 'b' to each side of the equation.
a + -1b + b + 4c = 0 + b

Combine like terms: -1b + b = 0
a + 0 + 4c = 0 + b
a + 4c = 0 + b
Remove the zero:
a + 4c = b

Add '-4c' to each side of the equation.
a + 4c + -4c = b + -4c

Combine like terms: 4c + -4c = 0
a + 0 = b + -4c
a = b + -4c

Simplifying
a = b + -4c
Solution
a = {0, b + -4c}

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