what is the zero-product propery?

Question

if 15xsqaured= 16x+15, what would the answer be? give a step by step explanation on how to do these types of problems.

Answer 1

15x^2=16x+15
move 15x^2 to the other side so that it will equal 0
-15x^2+16x+15=0
Factor it. trial and error thats how i do it. i could explain how to do it if u want me to.
(-3x+5)(5x+3)
after that use each factor and equal it to zero
-3x+5=0 , 5x+3=0
on -3x+5=0
isolate x, so that means subtract 5 from each side and divide it by -3..
x=-5/3
on 5x+3=0, do the same thing, subtract 3 from each sides and divide it by 5.. so
x=3/5

the answers are x=-5/3 and x=3/5

hope it helps.. if u need anymore just say it =]

Answer 2

you have to make it equal to zero (the zero product property basically says you can do that)
so the equation would read 15x^2-16x-15=0
then, you use the quadratic formula -b±(square root of b^2-4(a)(c)) (all over) 2a

in this a=15, b=-16, c=-15
so the equation is 16±(square root of -16^2-4(15)(-15) (all over) 2(15)

16±(square root of 256+900)(all over 30)
16±(square root of 1156) (all over 30)
16±(34)(all over 30)
8±17 (all over 15)
8+17 (all over 15) 8-17(all over 15)
25/15 -9/15
so x=1.66, -.6

Answer 3

15x² = 16x + 15

15x² - 16x - 15 = 0

Factor

(3x - 5)(5x + 3) = 0

x = 5/3, x = -3/5
.