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

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

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

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

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

Multiply (-4 + a) * (-5 + 3a)
(-4(-5 + 3a) + a(-5 + 3a)) = 0
((-5 * -4 + 3a * -4) + a(-5 + 3a)) = 0
((20 + -12a) + a(-5 + 3a)) = 0
(20 + -12a + (-5 * a + 3a * a)) = 0
(20 + -12a + (-5a + 3a2)) = 0

Combine like terms: -12a + -5a = -17a
(20 + -17a + 3a2) = 0

Solving
20 + -17a + 3a2 = 0

Solving for variable 'a'.

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

Subproblem 1
Set the factor '(5 + -3a)' equal to zero and attempt to solve:

Simplifying
5 + -3a = 0

Solving
5 + -3a = 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 + -3a = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3a = 0 + -5
-3a = 0 + -5

Combine like terms: 0 + -5 = -5
-3a = -5

Divide each side by '-3'.
a = 1.666666667

Simplifying
a = 1.666666667
Subproblem 2
Set the factor '(4 + -1a)' equal to zero and attempt to solve:

Simplifying
4 + -1a = 0

Solving
4 + -1a = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1a = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1a = 0 + -4
-1a = 0 + -4

Combine like terms: 0 + -4 = -4
-1a = -4

Divide each side by '-1'.
a = 4

Simplifying
a = 4
Solution
a = {1.666666667, 4}