4[2a-3a(2a+5b)+6a]=

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Solution for 4[2a-3a(2a+5b)+6a]= equation: 


Simplifying
4[2a + -3a(2a + 5b) + 6a] = 0
4[2a + (2a * -3a + 5b * -3a) + 6a] = 0

Reorder the terms:
4[2a + (-15ab + -6a2) + 6a] = 0
4[2a + (-15ab + -6a2) + 6a] = 0

Reorder the terms:
4[2a + 6a + -15ab + -6a2] = 0

Combine like terms: 2a + 6a = 8a
4[8a + -15ab + -6a2] = 0
[8a * 4 + -15ab * 4 + -6a2 * 4] = 0
[32a + -60ab + -24a2] = 0

Solving
32a + -60ab + -24a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '4a'.
4a(8 + -15b + -6a) = 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 '(8 + -15b + -6a)' equal to zero and attempt to solve:

Simplifying
8 + -15b + -6a = 0

Reorder the terms:
8 + -6a + -15b = 0

Solving
8 + -6a + -15b = 0

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

Add '-8' to each side of the equation.
8 + -6a + -8 + -15b = 0 + -8

Reorder the terms:
8 + -8 + -6a + -15b = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -6a + -15b = 0 + -8
-6a + -15b = 0 + -8

Combine like terms: 0 + -8 = -8
-6a + -15b = -8

Add '15b' to each side of the equation.
-6a + -15b + 15b = -8 + 15b

Combine like terms: -15b + 15b = 0
-6a + 0 = -8 + 15b
-6a = -8 + 15b

Divide each side by '-6'.
a = 1.333333333 + -2.5b

Simplifying
a = 1.333333333 + -2.5b
Solution
a = {0, 1.333333333 + -2.5b}

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