#### Answer

$\color{blue}{x=-1}$

#### Work Step by Step

Square both sides to obtain:
$3x+7=(3x+5)^2
\\3x+7=(3x)^2+2(3x)(5)+5^2
\\3x+7=9x^2+30x+25$
Move all terms to the left side of the equation.
Note that when a term is transferred to the other side of the equation, its sign changes to its opposite.
$0=9x^2+30x+25-3x-7
\\0=9x^2+27x+18
\\9x^2+27x+18=0$
Factor out $9$ to obtain:
$9(x^2+3x+2)=0$
Factor the trinomial to obtain:
$9(x+2)(x+1)=0$
Divide $9$ to both sides to obtain:
$(x+2)(x+1)=0$
Use the zero-factor property by equating each factor to zero.
$x+2=0$ or $x+1=0$
Solve each equation to obtain:
$x=-2$ or $x=-1$.
Upon checking, only $-1$ is a solution of the original equation.
Thus, the solution to the given equation is $\color{blue}{x=-1}$.