6a(2a-b)+2a(-4a+5b)=

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Solution for 6a(2a-b)+2a(-4a+5b)= equation: 


Simplifying
6a(2a + -1b) + 2a(-4a + 5b) = 0
(2a * 6a + -1b * 6a) + 2a(-4a + 5b) = 0

Reorder the terms:
(-6ab + 12a2) + 2a(-4a + 5b) = 0
(-6ab + 12a2) + 2a(-4a + 5b) = 0
-6ab + 12a2 + (-4a * 2a + 5b * 2a) = 0

Reorder the terms:
-6ab + 12a2 + (10ab + -8a2) = 0
-6ab + 12a2 + (10ab + -8a2) = 0

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

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

Combine like terms: 12a2 + -8a2 = 4a2
4ab + 4a2 = 0

Solving
4ab + 4a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '4a'.
4a(b + a) = 0

Ignore the factor 4.

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 + a)' equal to zero and attempt to solve:

Simplifying
b + a = 0

Reorder the terms:
a + b = 0

Solving
a + b = 0

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

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

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

Simplifying
a = -1b
Solution
a = {0, -1b}

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