4a(a-1)=15

Solution for 4a(a-1)=15 equation:

Simplifying
4a(a + -1) = 15

Reorder the terms:
4a(-1 + a) = 15
(-1 * 4a + a * 4a) = 15
(-4a + 4a2) = 15

Solving
-4a + 4a2 = 15

Solving for variable 'a'.

Reorder the terms:
-15 + -4a + 4a2 = 15 + -15

Combine like terms: 15 + -15 = 0
-15 + -4a + 4a2 = 0

Factor a trinomial.
(-3 + -2a)(5 + -2a) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(5 + -2a)' equal to zero and attempt to solve:

Simplifying
5 + -2a = 0

Solving
5 + -2a = 0

Move all terms containing a to the left, all other terms to the right.

Add '-5' to each side of the equation.
5 + -5 + -2a = 0 + -5

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

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

Divide each side by '-2'.
a = 2.5

Simplifying
a = 2.5
Solution
a = {-1.5, 2.5}