(3m+2n)(6m-4n)=18m2-8n2

Expand (3m+2n)(6m-4n) using the FOIL Method.

Apply the distributive property.

3m(6m-4n)+2n(6m-4n)=18m2-8n2

Apply the distributive property.

3m(6m)+3m(-4n)+2n(6m-4n)=18m2-8n2

Apply the distributive property.

3m(6m)+3m(-4n)+2n(6m)+2n(-4n)=18m2-8n2

3m(6m)+3m(-4n)+2n(6m)+2n(-4n)=18m2-8n2

Simplify and combine like terms.

Simplify each term.

Multiply m by m.

3⋅6m2+3m(-4n)+2n(6m)+2n(-4n)=18m2-8n2

Multiply 3 by 6.

18m2+3m(-4n)+2n(6m)+2n(-4n)=18m2-8n2

Rewrite using the commutative property of multiplication.

18m2+3⋅-4(mn)+2n(6m)+2n(-4n)=18m2-8n2

Multiply 3 by -4.

18m2-12(mn)+2n(6m)+2n(-4n)=18m2-8n2

Rewrite using the commutative property of multiplication.

18m2-12mn+2⋅6(nm)+2n(-4n)=18m2-8n2

Multiply 2 by 6.

18m2-12mn+12(nm)+2n(-4n)=18m2-8n2

Multiply n by n.

18m2-12mn+12nm+2⋅-4n2=18m2-8n2

Multiply 2 by -4.

18m2-12mn+12nm-8n2=18m2-8n2

18m2-12mn+12nm-8n2=18m2-8n2

Add -12mn and 12nm.

Move n.

18m2-12mn+12mn-8n2=18m2-8n2

Add -12mn and 12mn.

18m2+0-8n2=18m2-8n2

18m2+0-8n2=18m2-8n2

Add 18m2 and 0.

18m2-8n2=18m2-8n2

18m2-8n2=18m2-8n2

18m2-8n2=18m2-8n2

Subtract 18m2 from both sides of the equation.

18m2-8n2-18m2=-8n2

Combine the opposite terms in 18m2-8n2-18m2.

Subtract 18m2 from 18m2.

-8n2+0=-8n2

Add -8n2 and 0.

-8n2=-8n2

-8n2=-8n2

-8n2=-8n2

Divide each term in -8n2=-8n2 by -8.

-8n2-8=-8n2-8

Cancel the common factor of -8.

Cancel the common factor.

-8n2-8=-8n2-8

Divide n2 by 1.

n2=-8n2-8

n2=-8n2-8

Cancel the common factor of -8.

Cancel the common factor.

n2=-8n2-8

Divide n2 by 1.

n2=n2

n2=n2

n2=n2

Since the exponents are equal, the bases of the exponents on both sides of the equation must be equal.

|n|=|n|

Rewrite the absolute value equation as four equations without absolute value bars.

n=n

n=-(n)

-(n)=n

-(n)=-(n)

After simplifying, there are only two unique equations to be solved.

n=n

n=-(n)

Solve n=n for n.

Move all terms containing n to the left side of the equation.

Subtract n from both sides of the equation.

n-n=0

Subtract n from n.

0=0

0=0

Since 0=0, the equation will always be true.

Always true

Always true

Solve n=-(n) for n.

Multiply -1 by n.

n=-n

Move all terms containing n to the left side of the equation.

Add n to both sides of the equation.

n+n=0

Add n and n.

2n=0

2n=0

Divide each term by 2 and simplify.

Divide each term in 2n=0 by 2.

2n2=02

Cancel the common factor of 2.

Cancel the common factor.

2n2=02

Divide n by 1.

n=02

n=02

Divide 0 by 2.

n=0

n=0

n=0

List all of the solutions.

n=,0

n=,0

Solve for m (3m+2n)(6m-4n)=18m^2-8n^2