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

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


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

Reorder the terms:
(-12ab + 4ac + 8a2) + 2(2a + -3ab + -5ac) = 0
(-12ab + 4ac + 8a2) + 2(2a + -3ab + -5ac) = 0
-12ab + 4ac + 8a2 + (2a * 2 + -3ab * 2 + -5ac * 2) = 0
-12ab + 4ac + 8a2 + (4a + -6ab + -10ac) = 0

Reorder the terms:
4a + -12ab + -6ab + 4ac + -10ac + 8a2 = 0

Combine like terms: -12ab + -6ab = -18ab
4a + -18ab + 4ac + -10ac + 8a2 = 0

Combine like terms: 4ac + -10ac = -6ac
4a + -18ab + -6ac + 8a2 = 0

Solving
4a + -18ab + -6ac + 8a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2a'.
2a(2 + -9b + -3c + 4a) = 0

Ignore the factor 2.

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 '(2 + -9b + -3c + 4a)' equal to zero and attempt to solve:

Simplifying
2 + -9b + -3c + 4a = 0

Reorder the terms:
2 + 4a + -9b + -3c = 0

Solving
2 + 4a + -9b + -3c = 0

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

Add '-2' to each side of the equation.
2 + 4a + -9b + -2 + -3c = 0 + -2

Reorder the terms:
2 + -2 + 4a + -9b + -3c = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 4a + -9b + -3c = 0 + -2
4a + -9b + -3c = 0 + -2

Combine like terms: 0 + -2 = -2
4a + -9b + -3c = -2

Add '9b' to each side of the equation.
4a + -9b + 9b + -3c = -2 + 9b

Combine like terms: -9b + 9b = 0
4a + 0 + -3c = -2 + 9b
4a + -3c = -2 + 9b

Add '3c' to each side of the equation.
4a + -3c + 3c = -2 + 9b + 3c

Combine like terms: -3c + 3c = 0
4a + 0 = -2 + 9b + 3c
4a = -2 + 9b + 3c

Divide each side by '4'.
a = -0.5 + 2.25b + 0.75c

Simplifying
a = -0.5 + 2.25b + 0.75c
Solution
a = {0, -0.5 + 2.25b + 0.75c}

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