Solve the equation two 𝑥 minus
three multiplied by three 𝑥 plus four equals zero.
In this question, our quadratic
equation is already in a factored form. We are told that the product of two
linear expressions, two 𝑥 minus three and three 𝑥 plus four, is zero. And the only way this can happen is
if one or both of the factors individually is equal to zero. We have two possibilities: either
two 𝑥 minus three equals zero or three 𝑥 plus four equals zero.
We can solve the first equation by
firstly adding three to both sides. We can then divide through by two
such that 𝑥 is equal to three over two, or 1.5. We solve the second equation using
the same method. We subtract four from both sides
and then divide through by three. This gives us 𝑥 is equal to
negative four-thirds. The two solutions to the quadratic
equation two 𝑥 minus three multiplied by three 𝑥 plus four equals zero are 𝑥
equals three over two and 𝑥 equals negative four-thirds.