(3a-2)(4a+5)=0

Solution for (3a-2)(4a+5)=0 equation:

Simplifying
(3a + -2)(4a + 5) = 0

Reorder the terms:
(-2 + 3a)(4a + 5) = 0

Reorder the terms:
(-2 + 3a)(5 + 4a) = 0

Multiply (-2 + 3a) * (5 + 4a)
(-2(5 + 4a) + 3a * (5 + 4a)) = 0
((5 * -2 + 4a * -2) + 3a * (5 + 4a)) = 0
((-10 + -8a) + 3a * (5 + 4a)) = 0
(-10 + -8a + (5 * 3a + 4a * 3a)) = 0
(-10 + -8a + (15a + 12a2)) = 0

Combine like terms: -8a + 15a = 7a
(-10 + 7a + 12a2) = 0

Solving
-10 + 7a + 12a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-5 + -4a)(2 + -3a) = 0

Subproblem 1
Set the factor '(-5 + -4a)' equal to zero and attempt to solve:

Simplifying
-5 + -4a = 0

Solving
-5 + -4a = 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 + -4a = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -4a = 0 + 5
-4a = 0 + 5

Combine like terms: 0 + 5 = 5
-4a = 5

Divide each side by '-4'.
a = -1.25

Simplifying
a = -1.25
Subproblem 2
Set the factor '(2 + -3a)' equal to zero and attempt to solve:

Simplifying
2 + -3a = 0

Solving
2 + -3a = 0

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

Add '-2' to each side of the equation.
2 + -2 + -3a = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3a = 0 + -2
-3a = 0 + -2

Combine like terms: 0 + -2 = -2
-3a = -2

Divide each side by '-3'.
a = 0.6666666667

Simplifying
a = 0.6666666667
Solution
a = {-1.25, 0.6666666667}