Answer
$x=-7$
Work Step by Step
RECALL:
$(a+b)(c+d)=ac+ad+bc+bd$ (more popularly known as the FOIL method)
Use the FOIL method to obtain:
$(x+2)(x-5)=(x+1)(x-3)
\\x(x) + x(-5)+2(x) + 2(-5)=x(x)+x(-3)+1(x)+(1)(-3)
\\x^2-5x+2x-10=x^2-3x+x-3
\\x^2-3x-10=x^2-2x-3$
Put all the terms with a variable on the left side and the constants on the right side. Note that when you move a term from one side of the equation to the other, it changes to its opposite.
$x^2-3x-x^2+2x=-3+10
\\(x^2-x^2)+(-3x+2x)=7
\\0+(-x)=7
\\-x=7
\\-1(-x)=-1(7)
\\x=-7$