a-31a+5a+1a(a-3)=4a-8a(a-3)

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Solution for a-31a+5a+1a(a-3)=4a-8a(a-3) equation: 


Simplifying
a + -31a + 5a + 1a(a + -3) = 4a + -8a(a + -3)

Reorder the terms:
a + -31a + 5a + 1a(-3 + a) = 4a + -8a(a + -3)
a + -31a + 5a + (-3 * 1a + a * 1a) = 4a + -8a(a + -3)
a + -31a + 5a + (-3a + 1a2) = 4a + -8a(a + -3)

Combine like terms: a + -31a = -30a
-30a + 5a + -3a + 1a2 = 4a + -8a(a + -3)

Combine like terms: -30a + 5a = -25a
-25a + -3a + 1a2 = 4a + -8a(a + -3)

Combine like terms: -25a + -3a = -28a
-28a + 1a2 = 4a + -8a(a + -3)

Reorder the terms:
-28a + 1a2 = 4a + -8a(-3 + a)
-28a + 1a2 = 4a + (-3 * -8a + a * -8a)
-28a + 1a2 = 4a + (24a + -8a2)

Combine like terms: 4a + 24a = 28a
-28a + 1a2 = 28a + -8a2

Solving
-28a + 1a2 = 28a + -8a2

Solving for variable 'a'.

Reorder the terms:
-28a + -28a + 1a2 + 8a2 = 28a + -8a2 + -28a + 8a2

Combine like terms: -28a + -28a = -56a
-56a + 1a2 + 8a2 = 28a + -8a2 + -28a + 8a2

Combine like terms: 1a2 + 8a2 = 9a2
-56a + 9a2 = 28a + -8a2 + -28a + 8a2

Reorder the terms:
-56a + 9a2 = 28a + -28a + -8a2 + 8a2

Combine like terms: 28a + -28a = 0
-56a + 9a2 = 0 + -8a2 + 8a2
-56a + 9a2 = -8a2 + 8a2

Combine like terms: -8a2 + 8a2 = 0
-56a + 9a2 = 0

Factor out the Greatest Common Factor (GCF), 'a'.
a(-56 + 9a) = 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 '(-56 + 9a)' equal to zero and attempt to solve:

Simplifying
-56 + 9a = 0

Solving
-56 + 9a = 0

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

Add '56' to each side of the equation.
-56 + 56 + 9a = 0 + 56

Combine like terms: -56 + 56 = 0
0 + 9a = 0 + 56
9a = 0 + 56

Combine like terms: 0 + 56 = 56
9a = 56

Divide each side by '9'.
a = 6.222222222

Simplifying
a = 6.222222222
Solution
a = {0, 6.222222222}

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