Final answer:
The two solutions to the quadratic equation (3x + 4)(x - 9) = 0 are x = -4/3 and x = 9.
Explanation:
To find the solutions, we set each factor equal to zero and solve for x individually. First, setting 3x + 4 = 0, we get x = -4/3. Second, setting x - 9 = 0, we get x = 9. These are the solutions derived from the factored form of the quadratic equation.
When a product of factors equals zero, we apply the zero-product property, stating that if the product of factors equals zero, then at least one of the factors must be zero. This principle allows us to solve for x by equating each factor to zero separately. Therefore, x = -4/3 and x = 9 represent the two solutions for the given quadratic equation.
The two solutions to the quadratic equation (3x + 4)(x - 9) = 0 are x = -4/3 and x = 9.