# Question Video: Solving Quadratic Equations Written in Factorized Form Mathematics • 9th Grade

Solve the equation (2𝑥 − 3)(3𝑥 + 4) = 0.

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### Video Transcript

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.