c+2=15c+4

Since the radical is on the right side of the equation, switch the sides so it is on the left side of the equation.

15c+4=c+2

To remove the radical on the left side of the equation, square both sides of the equation.

15c+42=(c+2)2

Multiply the exponents in ((15c+4)12)2.

Apply the power rule and multiply exponents, (am)n=amn.

(15c+4)12⋅2=(c+2)2

Cancel the common factor of 2.

Cancel the common factor.

(15c+4)12⋅2=(c+2)2

Rewrite the expression.

(15c+4)1=(c+2)2

(15c+4)1=(c+2)2

(15c+4)1=(c+2)2

Simplify.

15c+4=(c+2)2

15c+4=(c+2)2

Simplify (c+2)2.

Rewrite (c+2)2 as (c+2)(c+2).

15c+4=(c+2)(c+2)

Expand (c+2)(c+2) using the FOIL Method.

Apply the distributive property.

15c+4=c(c+2)+2(c+2)

Apply the distributive property.

15c+4=c⋅c+c⋅2+2(c+2)

Apply the distributive property.

15c+4=c⋅c+c⋅2+2c+2⋅2

15c+4=c⋅c+c⋅2+2c+2⋅2

Simplify and combine like terms.

Simplify each term.

Multiply c by c.

15c+4=c2+c⋅2+2c+2⋅2

Move 2 to the left of c.

15c+4=c2+2⋅c+2c+2⋅2

Multiply 2 by 2.

15c+4=c2+2c+2c+4

15c+4=c2+2c+2c+4

Add 2c and 2c.

15c+4=c2+4c+4

15c+4=c2+4c+4

15c+4=c2+4c+4

Since c is on the right side of the equation, switch the sides so it is on the left side of the equation.

c2+4c+4=15c+4

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

Subtract 15c from both sides of the equation.

c2+4c+4-15c=4

Subtract 15c from 4c.

c2-11c+4=4

c2-11c+4=4

Move 4 to the left side of the equation by subtracting it from both sides.

c2-11c+4-4=0

Combine the opposite terms in c2-11c+4-4.

Subtract 4 from 4.

c2-11c+0=0

Add c2-11c and 0.

c2-11c=0

c2-11c=0

Factor c out of c2-11c.

Factor c out of c2.

c⋅c-11c=0

Factor c out of -11c.

c⋅c+c⋅-11=0

Factor c out of c⋅c+c⋅-11.

c(c-11)=0

c(c-11)=0

If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.

c=0

c-11=0

Set the first factor equal to 0.

c=0

Set the next factor equal to 0 and solve.

Set the next factor equal to 0.

c-11=0

Add 11 to both sides of the equation.

c=11

c=11

The final solution is all the values that make c(c-11)=0 true.

c=0,11

c=0,11

Solve for c c+2 = square root of 15c+4