Exercise 12 Page 86

To solve an equation, we should first gather all of the variable terms on one side of the equation and all of the constant terms on the other side, using the Properties of Equality. In this case, we need to start by using the Distributive Property to simplify the left- and right-hand sides of the equation.

3x(x+2)=3(x^2-2)

Distr

Distribute 3x

3x^2+6x=3(x^2-2)

Distr

Distribute 3

3x^2+6x=3x^2-6

Now we can continue to solve using the Properties of Equality.

3x^2+6x=3x^2-6

SubEqn

LHS-3x^2=RHS-3x^2

3x^2+6x-3x^2=3x^2-6-3x^2

SubTerms

Subtract terms

6x=- 6

DivEqn

.LHS /6.=.RHS /6.

6x/6=- 6/6

CalcQuot

Calculate quotient

x=- 1

The solution to the equation is x=- 1.