# Solve for m (m-4)/(m+20)=(m-20)/(4-m) m-4m+20=m-204-m
Multiply the numerator of the first fraction by the denominator of the second fraction. Set this equal to the product of the denominator of the first fraction and the numerator of the second fraction.
(m-4)⋅(4-m)=(m+20)⋅(m-20)
Solve the equation for m.
Simplify (m-4)⋅(4-m).
Expand (m-4)(4-m) using the FOIL Method.
Apply the distributive property.
m(4-m)-4(4-m)=(m+20)⋅(m-20)
Apply the distributive property.
m⋅4+m(-m)-4(4-m)=(m+20)⋅(m-20)
Apply the distributive property.
m⋅4+m(-m)-4⋅4-4(-m)=(m+20)⋅(m-20)
m⋅4+m(-m)-4⋅4-4(-m)=(m+20)⋅(m-20)
Simplify and combine like terms.
Simplify each term.
Move 4 to the left of m.
4⋅m+m(-m)-4⋅4-4(-m)=(m+20)⋅(m-20)
Rewrite using the commutative property of multiplication.
4m-m⋅m-4⋅4-4(-m)=(m+20)⋅(m-20)
Multiply m by m by adding the exponents.
Move m.
4m-(m⋅m)-4⋅4-4(-m)=(m+20)⋅(m-20)
Multiply m by m.
4m-m2-4⋅4-4(-m)=(m+20)⋅(m-20)
4m-m2-4⋅4-4(-m)=(m+20)⋅(m-20)
Multiply -4 by 4.
4m-m2-16-4(-m)=(m+20)⋅(m-20)
Multiply -1 by -4.
4m-m2-16+4m=(m+20)⋅(m-20)
4m-m2-16+4m=(m+20)⋅(m-20)
Add 4m and 4m.
8m-m2-16=(m+20)⋅(m-20)
8m-m2-16=(m+20)⋅(m-20)
8m-m2-16=(m+20)⋅(m-20)
Simplify (m+20)⋅(m-20).
Expand (m+20)(m-20) using the FOIL Method.
Apply the distributive property.
8m-m2-16=m(m-20)+20(m-20)
Apply the distributive property.
8m-m2-16=m⋅m+m⋅-20+20(m-20)
Apply the distributive property.
8m-m2-16=m⋅m+m⋅-20+20m+20⋅-20
8m-m2-16=m⋅m+m⋅-20+20m+20⋅-20
Simplify terms.
Combine the opposite terms in m⋅m+m⋅-20+20m+20⋅-20.
Reorder the factors in the terms m⋅-20 and 20m.
8m-m2-16=m⋅m-20m+20m+20⋅-20
Add -20m and 20m.
8m-m2-16=m⋅m+0+20⋅-20
Add m⋅m and 0.
8m-m2-16=m⋅m+20⋅-20
8m-m2-16=m⋅m+20⋅-20
Simplify each term.
Multiply m by m.
8m-m2-16=m2+20⋅-20
Multiply 20 by -20.
8m-m2-16=m2-400
8m-m2-16=m2-400
8m-m2-16=m2-400
8m-m2-16=m2-400
Move all terms containing m to the left side of the equation.
Subtract m2 from both sides of the equation.
8m-m2-16-m2=-400
Subtract m2 from -m2.
8m-2m2-16=-400
8m-2m2-16=-400
Set the equation equal to zero.
Move 400 to the left side of the equation by adding it to both sides.
8m-2m2-16+400=0
Add -16 and 400.
8m-2m2+384=0
8m-2m2+384=0
Factor the left side of the equation.
Factor 2 out of 8m-2m2+384.
Factor 2 out of 8m.
2(4m)-2m2+384
Factor 2 out of -2m2.
2(4m)+2(-m2)+384
Factor 2 out of 384.
2(4m)+2(-m2)+2(192)
Factor 2 out of 2(4m)+2(-m2).
2(4m-m2)+2(192)
Factor 2 out of 2(4m-m2)+2(192).
2(4m-m2+192)
2(4m-m2+192)
Let u=m. Substitute u for all occurrences of m.
2(4u-u2+192)
Factor by grouping.
Reorder terms.
2(-u2+4u+192)
For a polynomial of the form ax2+bx+c, rewrite the middle term as a sum of two terms whose product is a⋅c=-1⋅192=-192 and whose sum is b=4.
Factor 4 out of 4u.
2(-u2+4(u)+192)
Rewrite 4 as -12 plus 16
2(-u2+(-12+16)u+192)
Apply the distributive property.
2(-u2-12u+16u+192)
2(-u2-12u+16u+192)
Factor out the greatest common factor from each group.
Group the first two terms and the last two terms.
2((-u2-12u)+16u+192)
Factor out the greatest common factor (GCF) from each group.
2(u(-u-12)-16(-u-12))
2(u(-u-12)-16(-u-12))
Factor the polynomial by factoring out the greatest common factor, -u-12.
2((-u-12)(u-16))
2((-u-12)(u-16))
Factor.
Replace all occurrences of u with m.
2((-m-12)(m-16))
Remove unnecessary parentheses.
2(-m-12)(m-16)
2(-m-12)(m-16)
Replace the left side with the factored expression.
2(-m-12)(m-16)=0
2(-m-12)(m-16)=0
Divide each term in 2(-m-12)(m-16)=0 by 2.
2(-m-12)(m-16)2=02
Cancel the common factor of 2.
Cancel the common factor.
2(-m-12)(m-16)2=02
Divide (-m-12)(m-16) by 1.
(-m-12)(m-16)=02
(-m-12)(m-16)=02
Divide 0 by 2.
(-m-12)(m-16)=0
If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.
-m-12=0
m-16=0
Set the first factor equal to 0 and solve.
Set the first factor equal to 0.
-m-12=0
Add 12 to both sides of the equation.
-m=12
Multiply each term in -m=12 by -1
Multiply each term in -m=12 by -1.
(-m)⋅-1=12⋅-1
Multiply (-m)⋅-1.
Multiply -1 by -1.
1m=12⋅-1
Multiply m by 1.
m=12⋅-1
m=12⋅-1
Multiply 12 by -1.
m=-12
m=-12
m=-12
Set the next factor equal to 0 and solve.
Set the next factor equal to 0.
m-16=0
Add 16 to both sides of the equation.
m=16
m=16
The final solution is all the values that make 2(-m-12)(m-16)2=02 true.
m=-12,16
m=-12,16
Solve for m (m-4)/(m+20)=(m-20)/(4-m)

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