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

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
Simplify each side of the equation.
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
Solve for c.
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
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
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

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