(7a+11)(4a+12)+(15a+8)(7a+11)=0

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Solution for (7a+11)(4a+12)+(15a+8)(7a+11)=0 equation: 


Simplifying
(7a + 11)(4a + 12) + (15a + 8)(7a + 11) = 0

Reorder the terms:
(11 + 7a)(4a + 12) + (15a + 8)(7a + 11) = 0

Reorder the terms:
(11 + 7a)(12 + 4a) + (15a + 8)(7a + 11) = 0

Multiply (11 + 7a) * (12 + 4a)
(11(12 + 4a) + 7a * (12 + 4a)) + (15a + 8)(7a + 11) = 0
((12 * 11 + 4a * 11) + 7a * (12 + 4a)) + (15a + 8)(7a + 11) = 0
((132 + 44a) + 7a * (12 + 4a)) + (15a + 8)(7a + 11) = 0
(132 + 44a + (12 * 7a + 4a * 7a)) + (15a + 8)(7a + 11) = 0
(132 + 44a + (84a + 28a2)) + (15a + 8)(7a + 11) = 0

Combine like terms: 44a + 84a = 128a
(132 + 128a + 28a2) + (15a + 8)(7a + 11) = 0

Reorder the terms:
132 + 128a + 28a2 + (8 + 15a)(7a + 11) = 0

Reorder the terms:
132 + 128a + 28a2 + (8 + 15a)(11 + 7a) = 0

Multiply (8 + 15a) * (11 + 7a)
132 + 128a + 28a2 + (8(11 + 7a) + 15a * (11 + 7a)) = 0
132 + 128a + 28a2 + ((11 * 8 + 7a * 8) + 15a * (11 + 7a)) = 0
132 + 128a + 28a2 + ((88 + 56a) + 15a * (11 + 7a)) = 0
132 + 128a + 28a2 + (88 + 56a + (11 * 15a + 7a * 15a)) = 0
132 + 128a + 28a2 + (88 + 56a + (165a + 105a2)) = 0

Combine like terms: 56a + 165a = 221a
132 + 128a + 28a2 + (88 + 221a + 105a2) = 0

Reorder the terms:
132 + 88 + 128a + 221a + 28a2 + 105a2 = 0

Combine like terms: 132 + 88 = 220
220 + 128a + 221a + 28a2 + 105a2 = 0

Combine like terms: 128a + 221a = 349a
220 + 349a + 28a2 + 105a2 = 0

Combine like terms: 28a2 + 105a2 = 133a2
220 + 349a + 133a2 = 0

Solving
220 + 349a + 133a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(11 + 7a)(20 + 19a) = 0


Subproblem 1
Set the factor '(11 + 7a)' equal to zero and attempt to solve:

Simplifying
11 + 7a = 0

Solving
11 + 7a = 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 + 7a = 0 + -11

Combine like terms: 11 + -11 = 0
0 + 7a = 0 + -11
7a = 0 + -11

Combine like terms: 0 + -11 = -11
7a = -11

Divide each side by '7'.
a = -1.571428571

Simplifying
a = -1.571428571

Subproblem 2
Set the factor '(20 + 19a)' equal to zero and attempt to solve:

Simplifying
20 + 19a = 0

Solving
20 + 19a = 0

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

Add '-20' to each side of the equation.
20 + -20 + 19a = 0 + -20

Combine like terms: 20 + -20 = 0
0 + 19a = 0 + -20
19a = 0 + -20

Combine like terms: 0 + -20 = -20
19a = -20

Divide each side by '19'.
a = -1.052631579

Simplifying
a = -1.052631579
Solution
a = {-1.571428571, -1.052631579}

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