78-11a=(a-6)(a-6)

Solution for 78-11a=(a-6)(a-6) equation:

Simplifying
78 + -11a = (a + -6)(a + -6)

Reorder the terms:
78 + -11a = (-6 + a)(a + -6)

Reorder the terms:
78 + -11a = (-6 + a)(-6 + a)

Multiply (-6 + a) * (-6 + a)
78 + -11a = (-6(-6 + a) + a(-6 + a))
78 + -11a = ((-6 * -6 + a * -6) + a(-6 + a))
78 + -11a = ((36 + -6a) + a(-6 + a))
78 + -11a = (36 + -6a + (-6 * a + a * a))
78 + -11a = (36 + -6a + (-6a + a2))

Combine like terms: -6a + -6a = -12a
78 + -11a = (36 + -12a + a2)

Solving
78 + -11a = 36 + -12a + a2

Solving for variable 'a'.

Reorder the terms:
78 + -36 + -11a + 12a + -1a2 = 36 + -12a + a2 + -36 + 12a + -1a2

Combine like terms: 78 + -36 = 42
42 + -11a + 12a + -1a2 = 36 + -12a + a2 + -36 + 12a + -1a2

Combine like terms: -11a + 12a = 1a
42 + 1a + -1a2 = 36 + -12a + a2 + -36 + 12a + -1a2

Reorder the terms:
42 + 1a + -1a2 = 36 + -36 + -12a + 12a + a2 + -1a2

Combine like terms: 36 + -36 = 0
42 + 1a + -1a2 = 0 + -12a + 12a + a2 + -1a2
42 + 1a + -1a2 = -12a + 12a + a2 + -1a2

Combine like terms: -12a + 12a = 0
42 + 1a + -1a2 = 0 + a2 + -1a2
42 + 1a + -1a2 = a2 + -1a2

Combine like terms: a2 + -1a2 = 0
42 + 1a + -1a2 = 0

Factor a trinomial.
(7 + -1a)(6 + a) = 0

Subproblem 1
Set the factor '(7 + -1a)' equal to zero and attempt to solve:

Simplifying
7 + -1a = 0

Solving
7 + -1a = 0

Move all terms containing a to the left, all other terms to the right.

Add '-7' to each side of the equation.
7 + -7 + -1a = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1a = 0 + -7
-1a = 0 + -7

Combine like terms: 0 + -7 = -7
-1a = -7

Divide each side by '-1'.
a = 7

Simplifying
a = 7
Subproblem 2
Set the factor '(6 + a)' equal to zero and attempt to solve:

Simplifying
6 + a = 0

Solving
6 + a = 0

Move all terms containing a to the left, all other terms to the right.

Add '-6' to each side of the equation.
6 + -6 + a = 0 + -6

Combine like terms: 6 + -6 = 0
0 + a = 0 + -6
a = 0 + -6

Combine like terms: 0 + -6 = -6
a = -6

Simplifying
a = -6
Solution
a = {7, -6}