7(a-4)-a^2=19+3(a+3)

Solution for 7(a-4)-a^2=19+3(a+3) equation:

Simplifying
7(a + -4) + -1a2 = 19 + 3(a + 3)

Reorder the terms:
7(-4 + a) + -1a2 = 19 + 3(a + 3)
(-4 * 7 + a * 7) + -1a2 = 19 + 3(a + 3)
(-28 + 7a) + -1a2 = 19 + 3(a + 3)

Reorder the terms:
-28 + 7a + -1a2 = 19 + 3(3 + a)
-28 + 7a + -1a2 = 19 + (3 * 3 + a * 3)
-28 + 7a + -1a2 = 19 + (9 + 3a)

Combine like terms: 19 + 9 = 28
-28 + 7a + -1a2 = 28 + 3a

Solving
-28 + 7a + -1a2 = 28 + 3a

Solving for variable 'a'.

Reorder the terms:
-28 + -28 + 7a + -3a + -1a2 = 28 + 3a + -28 + -3a

Combine like terms: -28 + -28 = -56
-56 + 7a + -3a + -1a2 = 28 + 3a + -28 + -3a

Combine like terms: 7a + -3a = 4a
-56 + 4a + -1a2 = 28 + 3a + -28 + -3a

Reorder the terms:
-56 + 4a + -1a2 = 28 + -28 + 3a + -3a

Combine like terms: 28 + -28 = 0
-56 + 4a + -1a2 = 0 + 3a + -3a
-56 + 4a + -1a2 = 3a + -3a

Combine like terms: 3a + -3a = 0
-56 + 4a + -1a2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
56 + -4a + a2 = 0

Move the constant term to the right:

Add '-56' to each side of the equation.
56 + -4a + -56 + a2 = 0 + -56

Reorder the terms:
56 + -56 + -4a + a2 = 0 + -56

Combine like terms: 56 + -56 = 0
0 + -4a + a2 = 0 + -56
-4a + a2 = 0 + -56

Combine like terms: 0 + -56 = -56
-4a + a2 = -56

The a term is -4a.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4a + 4 + a2 = -56 + 4

Reorder the terms:
4 + -4a + a2 = -56 + 4

Combine like terms: -56 + 4 = -52
4 + -4a + a2 = -52

Factor a perfect square on the left side:
(a + -2)(a + -2) = -52

Can't calculate square root of the right side.

The solution to this equation could not be determined.