(5a-3)-(8a-6)a=11

Solution for (5a-3)-(8a-6)a=11 equation:

Simplifying
(5a + -3) + -1(8a + -6) * a = 11

Reorder the terms:
(-3 + 5a) + -1(8a + -6) * a = 11

Remove parenthesis around (-3 + 5a)
-3 + 5a + -1(8a + -6) * a = 11

Reorder the terms:
-3 + 5a + -1(-6 + 8a) * a = 11

Reorder the terms for easier multiplication:
-3 + 5a + -1a(-6 + 8a) = 11
-3 + 5a + (-6 * -1a + 8a * -1a) = 11
-3 + 5a + (6a + -8a2) = 11

Combine like terms: 5a + 6a = 11a
-3 + 11a + -8a2 = 11

Solving
-3 + 11a + -8a2 = 11

Solving for variable 'a'.

Reorder the terms:
-3 + -11 + 11a + -8a2 = 11 + -11

Combine like terms: -3 + -11 = -14
-14 + 11a + -8a2 = 11 + -11

Combine like terms: 11 + -11 = 0
-14 + 11a + -8a2 = 0

Begin completing the square.  Divide all terms by
-8 the coefficient of the squared term: 

Divide each side by '-8'.
1.75 + -1.375a + a2 = 0

Move the constant term to the right:

Add '-1.75' to each side of the equation.
1.75 + -1.375a + -1.75 + a2 = 0 + -1.75

Reorder the terms:
1.75 + -1.75 + -1.375a + a2 = 0 + -1.75

Combine like terms: 1.75 + -1.75 = 0.00
0.00 + -1.375a + a2 = 0 + -1.75
-1.375a + a2 = 0 + -1.75

Combine like terms: 0 + -1.75 = -1.75
-1.375a + a2 = -1.75

The a term is -1.375a.  Take half its coefficient (-0.6875).
Square it (0.47265625) and add it to both sides.

Add '0.47265625' to each side of the equation.
-1.375a + 0.47265625 + a2 = -1.75 + 0.47265625

Reorder the terms:
0.47265625 + -1.375a + a2 = -1.75 + 0.47265625

Combine like terms: -1.75 + 0.47265625 = -1.27734375
0.47265625 + -1.375a + a2 = -1.27734375

Factor a perfect square on the left side:
(a + -0.6875)(a + -0.6875) = -1.27734375

Can't calculate square root of the right side.

The solution to this equation could not be determined.