What is the solution(s) to this equation

y*2-8y+21=6

You mean to ask "What is/are the solution/s to this equation?"

y^2 - 8y + 21 = 6
y^2 - 8y + 15 = 0
(y - 5)(y - 3) = 0
y = 5 or y = 3

i'm assuming you meant to make it a quadratic equation, so it would be

y^2 - 8y + 21 = 6

the first step in solving a quadratic equation is to get everything on one side so that it equals 0. to do this, we'll subtract 6 from both sides

y^2 - 8y + 15 = 0

then, the we'll see if anything multiplies to equal 15 and adds to equal -8. to find this, we'll list the factors of 15

+/-1, +/-15
+/-3, +/-5

3 and 5 both multiply to give 15, and add to give -8 when they are negative. put each separate number in a parenthesis with y, so (y - 3)(y - 5) = 0

then, solve each set when they're set equal to 0, so

y - 3 = 0
y - 5 = 0

y = 3
y = 5

y = 3 and 5, and that is your solution to this equation.

Simple if that is y^2 - 8y + 21 = 6
Just subtract 6 from both sides
y^2 - 8y + 15 then you factor
Which will give you (y - 5)(y - 3) then make both equal to 0 to get the values of y, so y = 5 and y = 3

written alternatively: 15-6y = 0

answer: 5/2

just looked at the other answer...you meant y^2 (y squared), not y*2 (y times two)?