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McGraw Hill Integrated II, 2012
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McGraw Hill Integrated II, 2012 View details
5. Using the Distributive Property
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Exercise 40 Page 40

Use the Zero Product Property to solve the equation.

0, - 1

Practice makes perfect

We want to solve the given equation. At the end, we will check that our answer is correct.

Solving

2n(3n+3)=0 To do so, we will use the Zero Product Property.

2n(3n+3)=0
ZeroProdProp

Use the Zero Product Property

lc2n=0 & (I) 3n+3=0 & (II)
SubEqn

(II): LHS-3=RHS-3

lc2n=0 & (I) 3n=- 3 & (II)
DivEqn

(I): .LHS /2.=.RHS /2.

lcn=0 & (I) 3n=- 3 & (II)
DivEqn

(II): .LHS /3.=.RHS /3.

lcn=0 & (I) n=- 1 & (II)

We found that the solutions of the equation are 0 and - 1.

Checking

To check our answers, we will substitute them for n in the given equation. Let's start with n=0.

2n(3n+3)=0
Substitute

n= 0

2( 0)(3( 0)+3)? =0
ZeroPropMult

Zero Property of Multiplication

0(0+3)? =0
IdPropAdd

Identity Property of Addition

0(3)? =0
ZeroPropMult

Zero Property of Multiplication

0=0 ✓

Since substituting and solving resulted in a true statement, we know that n=0 is a solution of the equation. Let's now check n=- 1.

2n(3n+3)=0
Substitute

n= - 1

2( - 1)(3( - 1)+3)? =0
MultPosNeg

a(- b)=- a * b

2(-1)(- 3+3)? =0
AssociativePropAdd

Associative Property of Addition

2(-1)(3-3)? =0
DiffZero

3-3=0

2(-1)(0)? =0
ZeroPropMult

Zero Property of Multiplication

0=0 ✓

This is also a true statement, so we know that n=-1 is a solution of the equation.

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