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

Subproblem 1
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
Subproblem 2
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
Solution
a = {-0.6666666667, 1.25}