a^2=6a+7

Solution for a^2=6a+7 equation:

Simplifying
a2 = 6a + 7

Reorder the terms:
a2 = 7 + 6a

Solving
a2 = 7 + 6a

Solving for variable 'a'.

Reorder the terms:
-7 + -6a + a2 = 7 + 6a + -7 + -6a

Reorder the terms:
-7 + -6a + a2 = 7 + -7 + 6a + -6a

Combine like terms: 7 + -7 = 0
-7 + -6a + a2 = 0 + 6a + -6a
-7 + -6a + a2 = 6a + -6a

Combine like terms: 6a + -6a = 0
-7 + -6a + a2 = 0

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

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

Simplifying
-1 + -1a = 0

Solving
-1 + -1a = 0

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

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

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

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

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

Simplifying
a = -1
Subproblem 2
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
Solution
a = {-1, 7}