How to Solve the Exponential Equation (6 – x)^(x² + 7x + 12) = 1

Solve the exponential equation (6 – x)^(x² + 7x + 12) = 1
Solution to the exponential equation
Solution of this equation involve three different cases,
Case 1: 6 – x = 1
Case 2: 6 – x = -1 when x² + 7x + 12 = even number
Case 3: x² + 7x + 12 = 0 when 6 – x ≠ 0
Case 1
6 – x = 1
⇒ x = 5
Case 2
6 – x = -1
⇒ x = 7
Now check the answer by plugging the solution in x² + 7x + 12
x² + 7x + 12 = 7² + 7•7 + 12 = 49 + 49 + 12 = 110
⇒ x² + 7x + 12 is an even number
⇒ x = 7 is a solution
Case 3
x² + 7x + 12 is a quadratic equation, so we can solve this equation using factorization
x² + 7x + 12 = 0
⇒ x² + 3x + 4x + 12 = 0
⇒ x(x + 3) + 4(x + 3) = 0
so, (x + 3) (x + 4) = 0
thus, x = -3, -4
Now check the solution by plugging the solution in 6 – x
When x = -3
6 – x = 6 – (-3) = 9
6 – x ≠ 0, so x = -3 is a solution
When x = -4
6 – x = 6 – (-4) = 10
6 – x ≠ 0, so x = -4 is a solution
so we got x = 5, 7, -3 & -4