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

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

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

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

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

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

Solving for variable 'a'.

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

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

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

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

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

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}