(2a+5)(a+8)=0

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Solution for (2a+5)(a+8)=0 equation: 


Simplifying
(2a + 5)(a + 8) = 0

Reorder the terms:
(5 + 2a)(a + 8) = 0

Reorder the terms:
(5 + 2a)(8 + a) = 0

Multiply (5 + 2a) * (8 + a)
(5(8 + a) + 2a * (8 + a)) = 0
((8 * 5 + a * 5) + 2a * (8 + a)) = 0
((40 + 5a) + 2a * (8 + a)) = 0
(40 + 5a + (8 * 2a + a * 2a)) = 0
(40 + 5a + (16a + 2a2)) = 0

Combine like terms: 5a + 16a = 21a
(40 + 21a + 2a2) = 0

Solving
40 + 21a + 2a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(8 + a)(5 + 2a) = 0


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

Simplifying
8 + a = 0

Solving
8 + a = 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 + a = 0 + -8

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

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

Simplifying
a = -8

Subproblem 2
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
Solution
a = {-8, -2.5}

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