To expand the left side of the equation, we need to multiply (x+6) by itself:
(x+6)(x+6) = x^2 + 6x + 6x + 36= x^2 + 12x + 36
To expand the right side of the equation, we need to multiply (x-4) and (x+4), and then subtract 8:
(x-4)(x+4) - 8= x^2 + 4x - 4x - 16 - 8= x^2 - 24
Now, our equation becomes:
x^2 + 12x + 36 = x^2 - 24
Subtract x^2 from both sides:
12x + 36 = -24
Subtract 36 from both sides:
12x = -60
Divide by 12:
x = -5
Therefore, the solution to the equation is x = -5.
To expand the left side of the equation, we need to multiply (x+6) by itself:
(x+6)(x+6) = x^2 + 6x + 6x + 36
= x^2 + 12x + 36
To expand the right side of the equation, we need to multiply (x-4) and (x+4), and then subtract 8:
(x-4)(x+4) - 8
= x^2 + 4x - 4x - 16 - 8
= x^2 - 24
Now, our equation becomes:
x^2 + 12x + 36 = x^2 - 24
Subtract x^2 from both sides:
12x + 36 = -24
Subtract 36 from both sides:
12x = -60
Divide by 12:
x = -5
Therefore, the solution to the equation is x = -5.