Final answer:
To solve the equation, simplify both sides, eliminate fractions by cross-multiplying, and solve the resulting quadratic equation. The equation has two valid solutions.
Step-by-step explanation:
To solve the equation, we need to first simplify both sides. By multiplying the numerator and denominator of the left side by 3x+12, and the numerator and denominator of the right side by x+4, we get:
(10x+25)/(3x+12) = (5x)/(x+4)
Now, we can cross-multiply to eliminate the fractions:
(10x+25)(x+4) = (5x)(3x+12)
Expanding both sides and simplifying gives:
10x^2 + 40x + 25x + 100 = 15x^2 + 60x
Combining like terms and moving all the terms to one side, we get:
5x^2 + 25x - 100 = 0
Now, we can solve this quadratic equation. However, since there is no equal sign between the numerator and the denominator, we need to consider their zeros separately. Solving the equation gives two valid solutions:
x = -5 and x = 4
Therefore, the equation has two valid solutions.