(6a+2)(3a+7)=

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Solution for (6a+2)(3a+7)= equation: 


Simplifying
(6a + 2)(3a + 7) = 0

Reorder the terms:
(2 + 6a)(3a + 7) = 0

Reorder the terms:
(2 + 6a)(7 + 3a) = 0

Multiply (2 + 6a) * (7 + 3a)
(2(7 + 3a) + 6a * (7 + 3a)) = 0
((7 * 2 + 3a * 2) + 6a * (7 + 3a)) = 0
((14 + 6a) + 6a * (7 + 3a)) = 0
(14 + 6a + (7 * 6a + 3a * 6a)) = 0
(14 + 6a + (42a + 18a2)) = 0

Combine like terms: 6a + 42a = 48a
(14 + 48a + 18a2) = 0

Solving
14 + 48a + 18a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2'.
2(7 + 24a + 9a2) = 0

Factor a trinomial.
2((7 + 3a)(1 + 3a)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(7 + 3a)' equal to zero and attempt to solve:

Simplifying
7 + 3a = 0

Solving
7 + 3a = 0

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

Add '-7' to each side of the equation.
7 + -7 + 3a = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 3a = 0 + -7
3a = 0 + -7

Combine like terms: 0 + -7 = -7
3a = -7

Divide each side by '3'.
a = -2.333333333

Simplifying
a = -2.333333333

Subproblem 2
Set the factor '(1 + 3a)' equal to zero and attempt to solve:

Simplifying
1 + 3a = 0

Solving
1 + 3a = 0

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

Add '-1' to each side of the equation.
1 + -1 + 3a = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 3a = 0 + -1
3a = 0 + -1

Combine like terms: 0 + -1 = -1
3a = -1

Divide each side by '3'.
a = -0.3333333333

Simplifying
a = -0.3333333333
Solution
a = {-2.333333333, -0.3333333333}

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