(3a+1)(2a-5)=39

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Solution for (3a+1)(2a-5)=39 equation: 


Simplifying
(3a + 1)(2a + -5) = 39

Reorder the terms:
(1 + 3a)(2a + -5) = 39

Reorder the terms:
(1 + 3a)(-5 + 2a) = 39

Multiply (1 + 3a) * (-5 + 2a)
(1(-5 + 2a) + 3a * (-5 + 2a)) = 39
((-5 * 1 + 2a * 1) + 3a * (-5 + 2a)) = 39
((-5 + 2a) + 3a * (-5 + 2a)) = 39
(-5 + 2a + (-5 * 3a + 2a * 3a)) = 39
(-5 + 2a + (-15a + 6a2)) = 39

Combine like terms: 2a + -15a = -13a
(-5 + -13a + 6a2) = 39

Solving
-5 + -13a + 6a2 = 39

Solving for variable 'a'.

Reorder the terms:
-5 + -39 + -13a + 6a2 = 39 + -39

Combine like terms: -5 + -39 = -44
-44 + -13a + 6a2 = 39 + -39

Combine like terms: 39 + -39 = 0
-44 + -13a + 6a2 = 0

Factor a trinomial.
(-11 + -6a)(4 + -1a) = 0


Subproblem 1
Set the factor '(-11 + -6a)' equal to zero and attempt to solve:

Simplifying
-11 + -6a = 0

Solving
-11 + -6a = 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 + -6a = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -6a = 0 + 11
-6a = 0 + 11

Combine like terms: 0 + 11 = 11
-6a = 11

Divide each side by '-6'.
a = -1.833333333

Simplifying
a = -1.833333333

Subproblem 2
Set the factor '(4 + -1a)' equal to zero and attempt to solve:

Simplifying
4 + -1a = 0

Solving
4 + -1a = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1a = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1a = 0 + -4
-1a = 0 + -4

Combine like terms: 0 + -4 = -4
-1a = -4

Divide each side by '-1'.
a = 4

Simplifying
a = 4
Solution
a = {-1.833333333, 4}

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