(6a+5)(5a-6)=0

Solution for (6a+5)(5a-6)=0 equation:

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

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

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

Multiply (5 + 6a) * (-6 + 5a)
(5(-6 + 5a) + 6a * (-6 + 5a)) = 0
((-6 * 5 + 5a * 5) + 6a * (-6 + 5a)) = 0
((-30 + 25a) + 6a * (-6 + 5a)) = 0
(-30 + 25a + (-6 * 6a + 5a * 6a)) = 0
(-30 + 25a + (-36a + 30a2)) = 0

Combine like terms: 25a + -36a = -11a
(-30 + -11a + 30a2) = 0

Solving
-30 + -11a + 30a2 = 0

Solving for variable 'a'.

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

Subproblem 1
Set the factor '(-5 + -6a)' equal to zero and attempt to solve:

Simplifying
-5 + -6a = 0

Solving
-5 + -6a = 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 + -6a = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -6a = 0 + 5
-6a = 0 + 5

Combine like terms: 0 + 5 = 5
-6a = 5

Divide each side by '-6'.
a = -0.8333333333

Simplifying
a = -0.8333333333
Subproblem 2
Set the factor '(6 + -5a)' equal to zero and attempt to solve:

Simplifying
6 + -5a = 0

Solving
6 + -5a = 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 + -5a = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -5a = 0 + -6
-5a = 0 + -6

Combine like terms: 0 + -6 = -6
-5a = -6

Divide each side by '-5'.
a = 1.2

Simplifying
a = 1.2
Solution
a = {-0.8333333333, 1.2}