n-6n=12

Subtract n from both sides of the equation.

-6n=12-n

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

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

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