Question

Solve each equation. $$ 3 z(z-2)-z=3 z^{2}+4 $$

   Solve each equation.
$$
3 z(z-2)-z=3 z^{2}+4
$$

Prealgebra & Introductory Algebra

Prealgebra & Introductory Algebra

Julie Miller, Molly… 2nd Edition

Chapter 13, Problem 62

Instant Answer

Solved by Expert Erika Bustos

04/06/2022

Step 1

Step 1: First, we distribute the 3z in the left side of the equation: $$ 3z^2 - 6z - z = 3z^2 + 4 $$ Show more…

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Solve each equation. $$ 3 z(z-2)-z=3 z^{2}+4 $$

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Key Concepts

Distributive Property

The distributive property allows you to multiply a single term across terms inside parentheses. It is a fundamental algebraic property that helps in expanding expressions and simplifying equations by removing the parentheses, making it easier to combine like terms and solve the equation.

Combining Like Terms

Combining like terms involves gathering terms in an equation that have the same variable raised to the same power. This simplification step reduces the complexity of an equation, making it easier to isolate the variable and solve for it by minimizing redundant parts of the expression.

Balancing Equations

Balancing equations is the process of ensuring that any operation performed on one side of an equation is also performed on the other side. This property maintains the equality and is critical for correctly isolating the variable during the solving process.

Solving Linear Equations

Solving linear equations involves isolating the variable to determine its value by systematically simplifying the equation with algebraic operations. This process typically includes applying the distributive property, combining like terms, and performing inverse operations, which results in a straightforward solution for the variable.

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