Question

Solve each equation. $$ 12 y=8 y^{2} $$

   Solve each equation.
$$
12 y=8 y^{2}
$$

Algebra A Combined Function

Algebra A Combined Function

Elayn Martin-Gay 4th Edition

Chapter 6, Problem 61

Instant Answer

Solved by Expert Victor Salazar

02/09/2022

Step 1

Step 1: First, we can rewrite the equation as $8y^2 - 12y = 0$. Show more…

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Solve each equation. $$ 12 y=8 y^{2} $$

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Key Concepts

Zero Product Property

The Zero Product Property states that if the product of two (or more) factors is zero, then at least one of the factors must be zero. This principle is crucial in solving equations that have been factored, as it allows us to set each individual factor equal to zero to find the overall solutions.

Factoring

Factoring involves rewriting an algebraic expression as a product of simpler expressions. It’s a key technique in simplifying equations to a form where the Zero Product Property can be applied, making the process of finding solutions more straightforward.

Quadratic Equations

A quadratic equation is a second-degree polynomial equation of the form ax² + bx + c = 0. Techniques for solving quadratic equations include factoring, completing the square, or using the quadratic formula. Understanding how to manipulate and solve quadratic equations is a fundamental part of algebra.

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