7a-6=a^2+4

Solution for 7a-6=a^2+4 equation:

Simplifying
7a + -6 = a2 + 4

Reorder the terms:
-6 + 7a = a2 + 4

Reorder the terms:
-6 + 7a = 4 + a2

Solving
-6 + 7a = 4 + a2

Solving for variable 'a'.

Reorder the terms:
-6 + -4 + 7a + -1a2 = 4 + a2 + -4 + -1a2

Combine like terms: -6 + -4 = -10
-10 + 7a + -1a2 = 4 + a2 + -4 + -1a2

Reorder the terms:
-10 + 7a + -1a2 = 4 + -4 + a2 + -1a2

Combine like terms: 4 + -4 = 0
-10 + 7a + -1a2 = 0 + a2 + -1a2
-10 + 7a + -1a2 = a2 + -1a2

Combine like terms: a2 + -1a2 = 0
-10 + 7a + -1a2 = 0

Factor a trinomial.
(-5 + a)(2 + -1a) = 0

Subproblem 1
Set the factor '(-5 + a)' equal to zero and attempt to solve:

Simplifying
-5 + a = 0

Solving
-5 + a = 0

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

Add '5' to each side of the equation.
-5 + 5 + a = 0 + 5

Combine like terms: -5 + 5 = 0
0 + a = 0 + 5
a = 0 + 5

Combine like terms: 0 + 5 = 5
a = 5

Simplifying
a = 5
Subproblem 2
Set the factor '(2 + -1a)' equal to zero and attempt to solve:

Simplifying
2 + -1a = 0

Solving
2 + -1a = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1a = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1a = 0 + -2
-1a = 0 + -2

Combine like terms: 0 + -2 = -2
-1a = -2

Divide each side by '-1'.
a = 2

Simplifying
a = 2
Solution
a = {5, 2}