(5a^3-6a^2+3a)-(3a^2-8a^3+3a)=

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Solution for (5a^3-6a^2+3a)-(3a^2-8a^3+3a)= equation: 


Simplifying
(5a3 + -6a2 + 3a) + -1(3a2 + -8a3 + 3a) = 0

Reorder the terms:
(3a + -6a2 + 5a3) + -1(3a2 + -8a3 + 3a) = 0

Remove parenthesis around (3a + -6a2 + 5a3)
3a + -6a2 + 5a3 + -1(3a2 + -8a3 + 3a) = 0

Reorder the terms:
3a + -6a2 + 5a3 + -1(3a + 3a2 + -8a3) = 0
3a + -6a2 + 5a3 + (3a * -1 + 3a2 * -1 + -8a3 * -1) = 0
3a + -6a2 + 5a3 + (-3a + -3a2 + 8a3) = 0

Reorder the terms:
3a + -3a + -6a2 + -3a2 + 5a3 + 8a3 = 0

Combine like terms: 3a + -3a = 0
0 + -6a2 + -3a2 + 5a3 + 8a3 = 0
-6a2 + -3a2 + 5a3 + 8a3 = 0

Combine like terms: -6a2 + -3a2 = -9a2
-9a2 + 5a3 + 8a3 = 0

Combine like terms: 5a3 + 8a3 = 13a3
-9a2 + 13a3 = 0

Solving
-9a2 + 13a3 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), 'a2'.
a2(-9 + 13a) = 0


Subproblem 1
Set the factor 'a2' equal to zero and attempt to solve:

Simplifying
a2 = 0

Solving
a2 = 0

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

Simplifying
a2 = 0

Take the square root of each side:
a = {0}

Subproblem 2
Set the factor '(-9 + 13a)' equal to zero and attempt to solve:

Simplifying
-9 + 13a = 0

Solving
-9 + 13a = 0

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

Add '9' to each side of the equation.
-9 + 9 + 13a = 0 + 9

Combine like terms: -9 + 9 = 0
0 + 13a = 0 + 9
13a = 0 + 9

Combine like terms: 0 + 9 = 9
13a = 9

Divide each side by '13'.
a = 0.6923076923

Simplifying
a = 0.6923076923
Solution
a = {0, 0.6923076923}

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