## Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

$x=-7$
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. $x^2-3x-x^2+2x=-3+10 \\(x^2-x^2)+(-3x+2x)=7 \\0+(-x)=7 \\-x=7 \\-1(-x)=-1(7) \\x=-7$