(13a+8)(5a-15)=0

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Solution for (13a+8)(5a-15)=0 equation: 


Simplifying
(13a + 8)(5a + -15) = 0

Reorder the terms:
(8 + 13a)(5a + -15) = 0

Reorder the terms:
(8 + 13a)(-15 + 5a) = 0

Multiply (8 + 13a) * (-15 + 5a)
(8(-15 + 5a) + 13a * (-15 + 5a)) = 0
((-15 * 8 + 5a * 8) + 13a * (-15 + 5a)) = 0
((-120 + 40a) + 13a * (-15 + 5a)) = 0
(-120 + 40a + (-15 * 13a + 5a * 13a)) = 0
(-120 + 40a + (-195a + 65a2)) = 0

Combine like terms: 40a + -195a = -155a
(-120 + -155a + 65a2) = 0

Solving
-120 + -155a + 65a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-24 + -31a + 13a2) = 0

Factor a trinomial.
5((-8 + -13a)(3 + -1a)) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-8 + -13a)' equal to zero and attempt to solve:

Simplifying
-8 + -13a = 0

Solving
-8 + -13a = 0

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

Add '8' to each side of the equation.
-8 + 8 + -13a = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -13a = 0 + 8
-13a = 0 + 8

Combine like terms: 0 + 8 = 8
-13a = 8

Divide each side by '-13'.
a = -0.6153846154

Simplifying
a = -0.6153846154

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

Simplifying
3 + -1a = 0

Solving
3 + -1a = 0

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

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

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

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

Divide each side by '-1'.
a = 3

Simplifying
a = 3
Solution
a = {-0.6153846154, 3}

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