2a(a-3)-1(a-3)=0

Solution for 2a(a-3)-1(a-3)=0 equation:

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

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

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

Reorder the terms:
3 + -6a + -1a + 2a2 = 0

Combine like terms: -6a + -1a = -7a
3 + -7a + 2a2 = 0

Solving
3 + -7a + 2a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(1 + -2a)(3 + -1a) = 0

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

Simplifying
1 + -2a = 0

Solving
1 + -2a = 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 + -2a = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2a = 0 + -1
-2a = 0 + -1

Combine like terms: 0 + -1 = -1
-2a = -1

Divide each side by '-2'.
a = 0.5

Simplifying
a = 0.5
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 = {0.5, 3}