6(3a+4)+5(4a-2)a=5

Solution for 6(3a+4)+5(4a-2)a=5 equation:

Simplifying
6(3a + 4) + 5(4a + -2) * a = 5

Reorder the terms:
6(4 + 3a) + 5(4a + -2) * a = 5
(4 * 6 + 3a * 6) + 5(4a + -2) * a = 5
(24 + 18a) + 5(4a + -2) * a = 5

Reorder the terms:
24 + 18a + 5(-2 + 4a) * a = 5

Reorder the terms for easier multiplication:
24 + 18a + 5a(-2 + 4a) = 5
24 + 18a + (-2 * 5a + 4a * 5a) = 5
24 + 18a + (-10a + 20a2) = 5

Combine like terms: 18a + -10a = 8a
24 + 8a + 20a2 = 5

Solving
24 + 8a + 20a2 = 5

Solving for variable 'a'.

Reorder the terms:
24 + -5 + 8a + 20a2 = 5 + -5

Combine like terms: 24 + -5 = 19
19 + 8a + 20a2 = 5 + -5

Combine like terms: 5 + -5 = 0
19 + 8a + 20a2 = 0

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

Divide each side by '20'.
0.95 + 0.4a + a2 = 0.0

Move the constant term to the right:

Add '-0.95' to each side of the equation.
0.95 + 0.4a + -0.95 + a2 = 0.0 + -0.95

Reorder the terms:
0.95 + -0.95 + 0.4a + a2 = 0.0 + -0.95

Combine like terms: 0.95 + -0.95 = 0.00
0.00 + 0.4a + a2 = 0.0 + -0.95
0.4a + a2 = 0.0 + -0.95

Combine like terms: 0.0 + -0.95 = -0.95
0.4a + a2 = -0.95

The a term is 0.4a.  Take half its coefficient (0.2).
Square it (0.04) and add it to both sides.

Add '0.04' to each side of the equation.
0.4a + 0.04 + a2 = -0.95 + 0.04

Reorder the terms:
0.04 + 0.4a + a2 = -0.95 + 0.04

Combine like terms: -0.95 + 0.04 = -0.91
0.04 + 0.4a + a2 = -0.91

Factor a perfect square on the left side:
(a + 0.2)(a + 0.2) = -0.91

Can't calculate square root of the right side.

The solution to this equation could not be determined.