(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 = -11a
(-40 + -11a + 2a2) = 0

Solving
-40 + -11a + 2a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-5 + -2a)(8 + -1a) = 0


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 '(8 + -1a)' equal to zero and attempt to solve:

Simplifying
8 + -1a = 0

Solving
8 + -1a = 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 + -1a = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1a = 0 + -8
-1a = 0 + -8

Combine like terms: 0 + -8 = -8
-1a = -8

Divide each side by '-1'.
a = 8

Simplifying
a = 8
Solution
a = {-2.5, 8}

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