(a+3)(2a+1)=4a

Solution for (a+3)(2a+1)=4a equation:

Simplifying
(a + 3)(2a + 1) = 4a

Reorder the terms:
(3 + a)(2a + 1) = 4a

Reorder the terms:
(3 + a)(1 + 2a) = 4a

Multiply (3 + a) * (1 + 2a)
(3(1 + 2a) + a(1 + 2a)) = 4a
((1 * 3 + 2a * 3) + a(1 + 2a)) = 4a
((3 + 6a) + a(1 + 2a)) = 4a
(3 + 6a + (1 * a + 2a * a)) = 4a
(3 + 6a + (1a + 2a2)) = 4a

Combine like terms: 6a + 1a = 7a
(3 + 7a + 2a2) = 4a

Solving
3 + 7a + 2a2 = 4a

Solving for variable 'a'.

Reorder the terms:
3 + 7a + -4a + 2a2 = 4a + -4a

Combine like terms: 7a + -4a = 3a
3 + 3a + 2a2 = 4a + -4a

Combine like terms: 4a + -4a = 0
3 + 3a + 2a2 = 0

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
1.5 + 1.5a + a2 = 0

Move the constant term to the right:

Add '-1.5' to each side of the equation.
1.5 + 1.5a + -1.5 + a2 = 0 + -1.5

Reorder the terms:
1.5 + -1.5 + 1.5a + a2 = 0 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + 1.5a + a2 = 0 + -1.5
1.5a + a2 = 0 + -1.5

Combine like terms: 0 + -1.5 = -1.5
1.5a + a2 = -1.5

The a term is 1.5a.  Take half its coefficient (0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
1.5a + 0.5625 + a2 = -1.5 + 0.5625

Reorder the terms:
0.5625 + 1.5a + a2 = -1.5 + 0.5625

Combine like terms: -1.5 + 0.5625 = -0.9375
0.5625 + 1.5a + a2 = -0.9375

Factor a perfect square on the left side:
(a + 0.75)(a + 0.75) = -0.9375

Can't calculate square root of the right side.

The solution to this equation could not be determined.