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

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

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

Reorder the terms:
5a(-1 + a) = 2(a + 3)
(-1 * 5a + a * 5a) = 2(a + 3)
(-5a + 5a2) = 2(a + 3)

Reorder the terms:
-5a + 5a2 = 2(3 + a)
-5a + 5a2 = (3 * 2 + a * 2)
-5a + 5a2 = (6 + 2a)

Solving
-5a + 5a2 = 6 + 2a

Solving for variable 'a'.

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

Combine like terms: -5a + -2a = -7a
-6 + -7a + 5a2 = 6 + 2a + -6 + -2a

Reorder the terms:
-6 + -7a + 5a2 = 6 + -6 + 2a + -2a

Combine like terms: 6 + -6 = 0
-6 + -7a + 5a2 = 0 + 2a + -2a
-6 + -7a + 5a2 = 2a + -2a

Combine like terms: 2a + -2a = 0
-6 + -7a + 5a2 = 0

Factor a trinomial.
(-3 + -5a)(2 + -1a) = 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 + -1a)' equal to zero and attempt to solve:

Simplifying
2 + -1a = 0

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

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

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

Divide each side by '-1'.
a = 2

Simplifying
a = 2
Solution
a = {-0.6, 2}