a=3a(2b+5)(a-2b)

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Solution for a=3a(2b+5)(a-2b) equation: 


Simplifying
a = 3a(2b + 5)(a + -2b)

Reorder the terms:
a = 3a(5 + 2b)(a + -2b)

Multiply (5 + 2b) * (a + -2b)
a = 3a(5(a + -2b) + 2b * (a + -2b))
a = 3a((a * 5 + -2b * 5) + 2b * (a + -2b))
a = 3a((5a + -10b) + 2b * (a + -2b))
a = 3a(5a + -10b + (a * 2b + -2b * 2b))
a = 3a(5a + -10b + (2ab + -4b2))

Reorder the terms:
a = 3a(5a + 2ab + -10b + -4b2)
a = 3a(5a + 2ab + -10b + -4b2)
a = (5a * 3a + 2ab * 3a + -10b * 3a + -4b2 * 3a)

Reorder the terms:
a = (-30ab + -12ab2 + 15a2 + 6a2b)
a = (-30ab + -12ab2 + 15a2 + 6a2b)

Solving
a = -30ab + -12ab2 + 15a2 + 6a2b

Solving for variable 'a'.

Reorder the terms:
a + 30ab + 12ab2 + -15a2 + -6a2b = -30ab + 30ab + -12ab2 + 12ab2 + 15a2 + -15a2 + 6a2b + -6a2b

Combine like terms: -30ab + 30ab = 0
a + 30ab + 12ab2 + -15a2 + -6a2b = 0 + -12ab2 + 12ab2 + 15a2 + -15a2 + 6a2b + -6a2b
a + 30ab + 12ab2 + -15a2 + -6a2b = -12ab2 + 12ab2 + 15a2 + -15a2 + 6a2b + -6a2b

Combine like terms: -12ab2 + 12ab2 = 0
a + 30ab + 12ab2 + -15a2 + -6a2b = 0 + 15a2 + -15a2 + 6a2b + -6a2b
a + 30ab + 12ab2 + -15a2 + -6a2b = 15a2 + -15a2 + 6a2b + -6a2b

Combine like terms: 15a2 + -15a2 = 0
a + 30ab + 12ab2 + -15a2 + -6a2b = 0 + 6a2b + -6a2b
a + 30ab + 12ab2 + -15a2 + -6a2b = 6a2b + -6a2b

Combine like terms: 6a2b + -6a2b = 0
a + 30ab + 12ab2 + -15a2 + -6a2b = 0

Factor out the Greatest Common Factor (GCF), 'a'.
a(1 + 30b + 12b2 + -15a + -6ab) = 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 '(1 + 30b + 12b2 + -15a + -6ab)' equal to zero and attempt to solve:

Simplifying
1 + 30b + 12b2 + -15a + -6ab = 0

Reorder the terms:
1 + -15a + -6ab + 30b + 12b2 = 0

Solving
1 + -15a + -6ab + 30b + 12b2 = 0

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

Add '-1' to each side of the equation.
1 + -15a + -6ab + 30b + -1 + 12b2 = 0 + -1

Reorder the terms:
1 + -1 + -15a + -6ab + 30b + 12b2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -15a + -6ab + 30b + 12b2 = 0 + -1
-15a + -6ab + 30b + 12b2 = 0 + -1

Combine like terms: 0 + -1 = -1
-15a + -6ab + 30b + 12b2 = -1

Add '-30b' to each side of the equation.
-15a + -6ab + 30b + -30b + 12b2 = -1 + -30b

Combine like terms: 30b + -30b = 0
-15a + -6ab + 0 + 12b2 = -1 + -30b
-15a + -6ab + 12b2 = -1 + -30b

Add '-12b2' to each side of the equation.
-15a + -6ab + 12b2 + -12b2 = -1 + -30b + -12b2

Combine like terms: 12b2 + -12b2 = 0
-15a + -6ab + 0 = -1 + -30b + -12b2
-15a + -6ab = -1 + -30b + -12b2

The solution to this equation could not be determined.

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

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