(a-6)(2a+9)=0

Solution for (a-6)(2a+9)=0 equation:

Simplifying
(a + -6)(2a + 9) = 0

Reorder the terms:
(-6 + a)(2a + 9) = 0

Reorder the terms:
(-6 + a)(9 + 2a) = 0

Multiply (-6 + a) * (9 + 2a)
(-6(9 + 2a) + a(9 + 2a)) = 0
((9 * -6 + 2a * -6) + a(9 + 2a)) = 0
((-54 + -12a) + a(9 + 2a)) = 0
(-54 + -12a + (9 * a + 2a * a)) = 0
(-54 + -12a + (9a + 2a2)) = 0

Combine like terms: -12a + 9a = -3a
(-54 + -3a + 2a2) = 0

Solving
-54 + -3a + 2a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-9 + -2a)(6 + -1a) = 0

Subproblem 1
Set the factor '(-9 + -2a)' equal to zero and attempt to solve:

Simplifying
-9 + -2a = 0

Solving
-9 + -2a = 0

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

Add '9' to each side of the equation.
-9 + 9 + -2a = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -2a = 0 + 9
-2a = 0 + 9

Combine like terms: 0 + 9 = 9
-2a = 9

Divide each side by '-2'.
a = -4.5

Simplifying
a = -4.5
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
Solution
a = {-4.5, 6}