(12a+11)(4a+10)=0

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Solution for (12a+11)(4a+10)=0 equation: 


Simplifying
(12a + 11)(4a + 10) = 0

Reorder the terms:
(11 + 12a)(4a + 10) = 0

Reorder the terms:
(11 + 12a)(10 + 4a) = 0

Multiply (11 + 12a) * (10 + 4a)
(11(10 + 4a) + 12a * (10 + 4a)) = 0
((10 * 11 + 4a * 11) + 12a * (10 + 4a)) = 0
((110 + 44a) + 12a * (10 + 4a)) = 0
(110 + 44a + (10 * 12a + 4a * 12a)) = 0
(110 + 44a + (120a + 48a2)) = 0

Combine like terms: 44a + 120a = 164a
(110 + 164a + 48a2) = 0

Solving
110 + 164a + 48a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2'.
2(55 + 82a + 24a2) = 0

Factor a trinomial.
2((5 + 2a)(11 + 12a)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(5 + 2a)' equal to zero and attempt to solve:

Simplifying
5 + 2a = 0

Solving
5 + 2a = 0

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

Add '-5' to each side of the equation.
5 + -5 + 2a = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 2a = 0 + -5
2a = 0 + -5

Combine like terms: 0 + -5 = -5
2a = -5

Divide each side by '2'.
a = -2.5

Simplifying
a = -2.5

Subproblem 2
Set the factor '(11 + 12a)' equal to zero and attempt to solve:

Simplifying
11 + 12a = 0

Solving
11 + 12a = 0

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

Add '-11' to each side of the equation.
11 + -11 + 12a = 0 + -11

Combine like terms: 11 + -11 = 0
0 + 12a = 0 + -11
12a = 0 + -11

Combine like terms: 0 + -11 = -11
12a = -11

Divide each side by '12'.
a = -0.9166666667

Simplifying
a = -0.9166666667
Solution
a = {-2.5, -0.9166666667}

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