Final answer:
The solutions to the equation (3x-8)(x + 7) = 0 are found by setting each factor equal to zero. This yields the two solutions x = 8/3 and x = -7.
Step-by-step explanation:
To find the two solutions to the equation (3x-8)(x + 7) = 0, we need to make use of the property that if a product of two factors equals zero, at least one of the factors must themselves be equal to zero. That is, if A×B = 0, then either A = 0 or B = 0, or both.
So, for the equation given:
- The first factor is 3x-8. Setting this equal to zero gives us 3x-8 = 0. Adding 8 to both sides gives 3x = 8, and after dividing both sides by 3, we find x = 8/3, which simplifies to x ≈ 2.67.
- The second factor is x + 7. Setting this equal to zero gives us x + 7 = 0. Subtracting 7 from both sides gives us x = -7.
Therefore, the two solutions to the equation are x = 8/3 and x = -7.
It's always beneficial to check the answer to ensure it is reasonable. Substituting the found solutions into the original equation should result in zero.