6a^3-(7a^2b-2ab^2)=

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Solution for 6a^3-(7a^2b-2ab^2)= equation: 


Simplifying
6a3 + -1(7a2b + -2ab2) = 0

Reorder the terms:
6a3 + -1(-2ab2 + 7a2b) = 0
6a3 + (-2ab2 * -1 + 7a2b * -1) = 0
6a3 + (2ab2 + -7a2b) = 0

Reorder the terms:
2ab2 + -7a2b + 6a3 = 0

Solving
2ab2 + -7a2b + 6a3 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), 'a'.
a(2b2 + -7ab + 6a2) = 0

Factor a trinomial.
a((b + -2a)(2b + -3a)) = 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 '(b + -2a)' equal to zero and attempt to solve:

Simplifying
b + -2a = 0

Reorder the terms:
-2a + b = 0

Solving
-2a + b = 0

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

Add '-1b' to each side of the equation.
-2a + b + -1b = 0 + -1b

Combine like terms: b + -1b = 0
-2a + 0 = 0 + -1b
-2a = 0 + -1b
Remove the zero:
-2a = -1b

Divide each side by '-2'.
a = 0.5b

Simplifying
a = 0.5b

Subproblem 3
Set the factor '(2b + -3a)' equal to zero and attempt to solve:

Simplifying
2b + -3a = 0

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

Solving
-3a + 2b = 0

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

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

Combine like terms: 2b + -2b = 0
-3a + 0 = 0 + -2b
-3a = 0 + -2b
Remove the zero:
-3a = -2b

Divide each side by '-3'.
a = 0.6666666667b

Simplifying
a = 0.6666666667b
Solution
a = {0, 0.5b, 0.6666666667b}

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