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

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

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

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

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

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

Combine like terms: -12a + 15a = 3a
(-15 + 3a + 12a2) = 0

Solving
-15 + 3a + 12a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-5 + a + 4a2) = 0

Factor a trinomial.
3((-5 + -4a)(1 + -1a)) = 0

Ignore the factor 3.
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 '(1 + -1a)' equal to zero and attempt to solve:

Simplifying
1 + -1a = 0

Solving
1 + -1a = 0

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

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

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

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

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

Simplifying
a = 1
Solution
a = {-1.25, 1}