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

(3m+2n)(6m-4n)=18m2-8n2
Simplify (3m+2n)(6m-4n).
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
Move n.
18m2-12mn+12mn-8n2=18m2-8n2
18m2+0-8n2=18m2-8n2
18m2+0-8n2=18m2-8n2
18m2-8n2=18m2-8n2
18m2-8n2=18m2-8n2
18m2-8n2=18m2-8n2
Move all terms containing m to the left side of the equation.
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
-8n2=-8n2
-8n2=-8n2
-8n2=-8n2
Divide each term by -8 and simplify.
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|
Solve for 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
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

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