# Solve for n n- square root of 6n=12 n-6n=12
Subtract n from both sides of the equation.
-6n=12-n
Multiply each term in -6n=12-n by -1
Multiply each term in -6n=12-n by -1.
(-6n)⋅-1=12⋅-1+(-n)⋅-1
Multiply -6n⋅-1.
Multiply -1 by -1.
16n=12⋅-1+(-n)⋅-1
Multiply 6n by 1.
6n=12⋅-1+(-n)⋅-1
6n=12⋅-1+(-n)⋅-1
Simplify each term.
Multiply 12 by -1.
6n=-12+(-n)⋅-1
Multiply (-n)⋅-1.
Multiply -1 by -1.
6n=-12+1n
Multiply n by 1.
6n=-12+n
6n=-12+n
6n=-12+n
6n=-12+n
To remove the radical on the left side of the equation, square both sides of the equation.
6n2=(-12+n)2
Simplify each side of the equation.
Multiply the exponents in ((6n)12)2.
Apply the power rule and multiply exponents, (am)n=amn.
(6n)12⋅2=(-12+n)2
Cancel the common factor of 2.
Cancel the common factor.
(6n)12⋅2=(-12+n)2
Rewrite the expression.
(6n)1=(-12+n)2
(6n)1=(-12+n)2
(6n)1=(-12+n)2
Simplify.
6n=(-12+n)2
6n=(-12+n)2
Solve for n.
Simplify (-12+n)2.
Rewrite (-12+n)2 as (-12+n)(-12+n).
6n=(-12+n)(-12+n)
Expand (-12+n)(-12+n) using the FOIL Method.
Apply the distributive property.
6n=-12(-12+n)+n(-12+n)
Apply the distributive property.
6n=-12⋅-12-12n+n(-12+n)
Apply the distributive property.
6n=-12⋅-12-12n+n⋅-12+n⋅n
6n=-12⋅-12-12n+n⋅-12+n⋅n
Simplify and combine like terms.
Simplify each term.
Multiply -12 by -12.
6n=144-12n+n⋅-12+n⋅n
Move -12 to the left of n.
6n=144-12n-12⋅n+n⋅n
Multiply n by n.
6n=144-12n-12n+n2
6n=144-12n-12n+n2
Subtract 12n from -12n.
6n=144-24n+n2
6n=144-24n+n2
6n=144-24n+n2
Since n is on the right side of the equation, switch the sides so it is on the left side of the equation.
144-24n+n2=6n
Move all terms containing n to the left side of the equation.
Subtract 6n from both sides of the equation.
144-24n+n2-6n=0
Subtract 6n from -24n.
144+n2-30n=0
144+n2-30n=0
Factor 144+n2-30n using the AC method.
Consider the form x2+bx+c. Find a pair of integers whose product is c and whose sum is b. In this case, whose product is 144 and whose sum is -30.
-24,-6
Write the factored form using these integers.
(n-24)(n-6)=0
(n-24)(n-6)=0
If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.
n-24=0
n-6=0
Set the first factor equal to 0 and solve.
Set the first factor equal to 0.
n-24=0
Add 24 to both sides of the equation.
n=24
n=24
Set the next factor equal to 0 and solve.
Set the next factor equal to 0.
n-6=0
Add 6 to both sides of the equation.
n=6
n=6
The final solution is all the values that make (n-24)(n-6)=0 true.
n=24,6
n=24,6
Exclude the solutions that do not make n-6n=12 true.
n=24
Solve for n n- square root of 6n=12

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