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

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

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

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

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

Multiply (3 + 5a) * (-2 + 3a)
(3(-2 + 3a) + 5a * (-2 + 3a)) = 0
((-2 * 3 + 3a * 3) + 5a * (-2 + 3a)) = 0
((-6 + 9a) + 5a * (-2 + 3a)) = 0
(-6 + 9a + (-2 * 5a + 3a * 5a)) = 0
(-6 + 9a + (-10a + 15a2)) = 0

Combine like terms: 9a + -10a = -1a
(-6 + -1a + 15a2) = 0

Solving
-6 + -1a + 15a2 = 0

Solving for variable 'a'.

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

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

Simplifying
-3 + -5a = 0

Solving
-3 + -5a = 0

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

Add '3' to each side of the equation.
-3 + 3 + -5a = 0 + 3

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

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

Divide each side by '-5'.
a = -0.6

Simplifying
a = -0.6
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 = {-0.6, 0.6666666667}