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.
$2 x^2+14 x=36$

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Key Concepts

Greatest Common Factor (GCF)

Factoring an expression often starts with identifying and extracting the greatest common factor, which is the largest factor shared by all terms in the expression. Removing the GCF simplifies the expression and can make further factoring steps more apparent.

Factoring Techniques

Once the equation is rewritten in standard form with zero on one side, various factoring techniques are applied to break down the expression into simpler binomial or monomial factors. This process is crucial for solving polynomial equations, as it enables the use of the zero-product property.

Setting Equations to Zero

This concept involves rearranging an equation so that one side of the equation is zero. By doing this, the equation is simplified into a standard form that is easier to work with, particularly when it comes to factoring and finding the roots of the equation.

Zero-Product Property

After factoring the quadratic equation, the zero-product property is used. This property states that if the product of two or more factors equals zero, then at least one of the factors must be zero. This principle is essential for finding the solutions to the equation.

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