3a*4b+7*2ab+a*6a+8ab*3=

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Solution for 3a*4b+7*2ab+a*6a+8ab*3= equation: 


Simplifying
3a * 4b + 7 * 2ab + a * 6a + 8ab * 3 = 0

Reorder the terms for easier multiplication:
3 * 4a * b + 7 * 2ab + a * 6a + 8ab * 3 = 0

Multiply 3 * 4
12a * b + 7 * 2ab + a * 6a + 8ab * 3 = 0

Multiply a * b
12ab + 7 * 2ab + a * 6a + 8ab * 3 = 0

Multiply 7 * 2
12ab + 14ab + a * 6a + 8ab * 3 = 0

Reorder the terms for easier multiplication:
12ab + 14ab + 6a * a + 8ab * 3 = 0

Multiply a * a
12ab + 14ab + 6a2 + 8ab * 3 = 0

Reorder the terms for easier multiplication:
12ab + 14ab + 6a2 + 8 * 3ab = 0

Multiply 8 * 3
12ab + 14ab + 6a2 + 24ab = 0

Reorder the terms:
12ab + 14ab + 24ab + 6a2 = 0

Combine like terms: 12ab + 14ab = 26ab
26ab + 24ab + 6a2 = 0

Combine like terms: 26ab + 24ab = 50ab
50ab + 6a2 = 0

Solving
50ab + 6a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2a'.
2a(25b + 3a) = 0

Ignore the factor 2.

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 '(25b + 3a)' equal to zero and attempt to solve:

Simplifying
25b + 3a = 0

Reorder the terms:
3a + 25b = 0

Solving
3a + 25b = 0

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

Add '-25b' to each side of the equation.
3a + 25b + -25b = 0 + -25b

Combine like terms: 25b + -25b = 0
3a + 0 = 0 + -25b
3a = 0 + -25b
Remove the zero:
3a = -25b

Divide each side by '3'.
a = -8.333333333b

Simplifying
a = -8.333333333b
Solution
a = {0, -8.333333333b}

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