Final answer:
To solve the given equation, take the logarithm with base 12 on both sides, simplify the equation, and solve for x by factoring the quadratic equation.
Step-by-step explanation:
To solve the equation 12(x²+5x-4) = 12(2x+6), we can start by taking the logarithm of both sides with base 12. This will allow us to simplify the equation and solve for x. Using the property of logarithms, we can bring down the exponents as coefficients, so we have (x²+5x-4) = (2x+6). Now, we can rearrange the equation to simplify it further:
x²+5x-4 = 2x+6
Next, we can bring all the terms to one side of the equation:
x²+5x-2x-4-6 = 0
Simplifying further, we have:
x²+3x-10 = 0
Now, we can factor this quadratic equation:
(x+5)(x-2) = 0
Setting each factor equal to zero, we have:
x+5 = 0, x-2 = 0
Solving for x, we get:
x = -5, x = 2