For the following exercises, solve the equation by...

For the following exercises, solve the equation by factoring. You will need to set the equation equal to 0 first, then find the greatest common factor, and finally see if further factoring is possible.
$5 x^2=5 x+30$

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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 used after the polynomial is factored to set each individual factor equal to zero, thereby deriving the solutions of the original equation.

Factoring Techniques

This concept involves expressing a polynomial as a product of its factors. Factoring techniques are applied after rewriting the equation in standard form, and may include grouping, trinomial factoring, or simply recognizing patterns. These methods are used to break down the equation into simpler factors that can be solved individually.

Greatest Common Factor (GCF)

Finding the greatest common factor entails identifying the largest factor that is common to all terms in the equation. Extracting the GCF simplifies the problem and sometimes reveals additional factorable structures, making the subsequent factoring process more straightforward.

Standard Form Transformation

This involves rewriting an equation such that one side is zero, yielding the standard form of a polynomial (usually quadratic) equation. This step is essential because most factoring methods and the zero product property require the equation to be set to zero in order to directly find solutions.

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