Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 5 - Cumulative Review - Page 334: 50


$x=-\frac{2}{3} \text{ or } x=4$

Work Step by Step

There is a need to factor the trinomial on the left side of the equation. The product of the leading term (3) and the constant term (-8) is $-24$. The factors of $-24$ whose sum is equal to the coefficient of the middle term, which is $-10$, are $2$ and $-12$. Write the middle using these factors to have: $\\3x^2+2x-12x-8=0$ Regroup to have: $\\(3x^2+2x)+(-12x-8)=0$ Factor out the GCF of each group to have: $\\x(3x+2)+(-4)(3x+2)=0 \\(3x+2)(x-4)=0$ Equate each factor to zero then solve each equation to have: $\\3x+2=0 \text{ or } x-4=0 \\3x=-2 \text{ or } x=4 \\x=-\frac{2}{3} \text{ or } x=4$
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