(2a-5)(3a+1)-(3a+1)(a-2)=

Solution for (2a-5)(3a+1)-(3a+1)(a-2)= equation:

Simplifying
(2a + -5)(3a + 1) + -1(3a + 1)(a + -2) = 0

Reorder the terms:
(-5 + 2a)(3a + 1) + -1(3a + 1)(a + -2) = 0

Reorder the terms:
(-5 + 2a)(1 + 3a) + -1(3a + 1)(a + -2) = 0

Multiply (-5 + 2a) * (1 + 3a)
(-5(1 + 3a) + 2a * (1 + 3a)) + -1(3a + 1)(a + -2) = 0
((1 * -5 + 3a * -5) + 2a * (1 + 3a)) + -1(3a + 1)(a + -2) = 0
((-5 + -15a) + 2a * (1 + 3a)) + -1(3a + 1)(a + -2) = 0
(-5 + -15a + (1 * 2a + 3a * 2a)) + -1(3a + 1)(a + -2) = 0
(-5 + -15a + (2a + 6a2)) + -1(3a + 1)(a + -2) = 0

Combine like terms: -15a + 2a = -13a
(-5 + -13a + 6a2) + -1(3a + 1)(a + -2) = 0

Reorder the terms:
-5 + -13a + 6a2 + -1(1 + 3a)(a + -2) = 0

Reorder the terms:
-5 + -13a + 6a2 + -1(1 + 3a)(-2 + a) = 0

Multiply (1 + 3a) * (-2 + a)
-5 + -13a + 6a2 + -1(1(-2 + a) + 3a * (-2 + a)) = 0
-5 + -13a + 6a2 + -1((-2 * 1 + a * 1) + 3a * (-2 + a)) = 0
-5 + -13a + 6a2 + -1((-2 + 1a) + 3a * (-2 + a)) = 0
-5 + -13a + 6a2 + -1(-2 + 1a + (-2 * 3a + a * 3a)) = 0
-5 + -13a + 6a2 + -1(-2 + 1a + (-6a + 3a2)) = 0

Combine like terms: 1a + -6a = -5a
-5 + -13a + 6a2 + -1(-2 + -5a + 3a2) = 0
-5 + -13a + 6a2 + (-2 * -1 + -5a * -1 + 3a2 * -1) = 0
-5 + -13a + 6a2 + (2 + 5a + -3a2) = 0

Reorder the terms:
-5 + 2 + -13a + 5a + 6a2 + -3a2 = 0

Combine like terms: -5 + 2 = -3
-3 + -13a + 5a + 6a2 + -3a2 = 0

Combine like terms: -13a + 5a = -8a
-3 + -8a + 6a2 + -3a2 = 0

Combine like terms: 6a2 + -3a2 = 3a2
-3 + -8a + 3a2 = 0

Solving
-3 + -8a + 3a2 = 0

Solving for variable 'a'.

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

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

Simplifying
-1 + -3a = 0

Solving
-1 + -3a = 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 + -3a = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -3a = 0 + 1
-3a = 0 + 1

Combine like terms: 0 + 1 = 1
-3a = 1

Divide each side by '-3'.
a = -0.3333333333

Simplifying
a = -0.3333333333
Subproblem 2
Set the factor '(3 + -1a)' equal to zero and attempt to solve:

Simplifying
3 + -1a = 0

Solving
3 + -1a = 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 + -1a = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1a = 0 + -3
-1a = 0 + -3

Combine like terms: 0 + -3 = -3
-1a = -3

Divide each side by '-1'.
a = 3

Simplifying
a = 3
Solution
a = {-0.3333333333, 3}