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

Subproblem 1
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
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 = {-2.5, 1.5}