Answer
$\{ -5,4\}$.
Work Step by Step
The given equation is
$x(x+9)=4(2x+5)$
Subtract $4(2x+5)$ from both sides.
$x(x+9)-4(2x+5)=4(2x+5)-4(2x+5)$
Simplify.
$x(x+9)-4(2x+5)=0$
Use the distributive property.
$x^2+9x-8x-20=0$
Add like terms.
$x^2+x-20=0$
Rewrite the middle term $x$ as $5x-4x$.
$x^2+5x-4x-20=0$
Group terms.
$(x^2+5x)+(-4x-20)=0$
Factor each term.
$x(x+5)-4(x+5)=0$
Factor out $(x+5)$.
$(x+5)(x-4)=0$
Set each factor equal to zero.
$x+5=0$ or $x-4=0$
Isolate $x$.
$x=-5$ or $x=4$
Check the solution.
Substitute $x=-5$ into the equation.
$(-5)(-5+9)=4(2(-5)+5)$
Solve both sides.
$(-5)(4)=4(-10+5)$
$-20=4(-5)$
$-20=-20$ True.
Check the solution.
Substitute $x=4$ into the equation.
$(4)(4+9)=4(2(4)+5)$
Solve both sides.
$(4)(13)=4(8+5)$
$52=4(13)$
$52=52$ True.
Hence, the solution set is $\{ -5,4\}$.
