(a+6)(2a^2-5a)=

Solution for (a+6)(2a^2-5a)= equation:

Simplifying
(a + 6)(2a2 + -5a) = 0

Reorder the terms:
(6 + a)(2a2 + -5a) = 0

Reorder the terms:
(6 + a)(-5a + 2a2) = 0

Multiply (6 + a) * (-5a + 2a2)
(6(-5a + 2a2) + a(-5a + 2a2)) = 0
((-5a * 6 + 2a2 * 6) + a(-5a + 2a2)) = 0
((-30a + 12a2) + a(-5a + 2a2)) = 0
(-30a + 12a2 + (-5a * a + 2a2 * a)) = 0
(-30a + 12a2 + (-5a2 + 2a3)) = 0

Combine like terms: 12a2 + -5a2 = 7a2
(-30a + 7a2 + 2a3) = 0

Solving
-30a + 7a2 + 2a3 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), 'a'.
a(-30 + 7a + 2a2) = 0

Factor a trinomial.
a((-6 + -1a)(5 + -2a)) = 0

Subproblem 1
Set the factor 'a' equal to zero and attempt to solve:

Simplifying
a = 0

Solving
a = 0

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

Simplifying
a = 0
Subproblem 2
Set the factor '(-6 + -1a)' equal to zero and attempt to solve:

Simplifying
-6 + -1a = 0

Solving
-6 + -1a = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1a = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1a = 0 + 6
-1a = 0 + 6

Combine like terms: 0 + 6 = 6
-1a = 6

Divide each side by '-1'.
a = -6

Simplifying
a = -6
Subproblem 3
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 = {0, -6, 2.5}