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

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

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

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

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

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

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

Solving
-3 + -1a + 2a2 = 0

Solving for variable 'a'.

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

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

Simplifying
3 + -2a = 0

Solving
3 + -2a = 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 + -2a = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2a = 0 + -3
-2a = 0 + -3

Combine like terms: 0 + -3 = -3
-2a = -3

Divide each side by '-2'.
a = 1.5

Simplifying
a = 1.5
Solution
a = {-1, 1.5}