4a(a+1)=3

Solution for 4a(a+1)=3 equation:

Simplifying
4a(a + 1) = 3

Reorder the terms:
4a(1 + a) = 3
(1 * 4a + a * 4a) = 3
(4a + 4a2) = 3

Solving
4a + 4a2 = 3

Solving for variable 'a'.

Reorder the terms:
-3 + 4a + 4a2 = 3 + -3

Combine like terms: 3 + -3 = 0
-3 + 4a + 4a2 = 0

Factor a trinomial.
(-3 + -2a)(1 + -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 '(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
Solution
a = {-1.5, 0.5}