solving ratios with 2 variables?

Question

After I used cross products on a ratio, I got this answere:
t² + t - 6 = 2t

What do I do next?

Answer 1

Just solve for t using factorization:

t² - t - 6 = 0
(t - 3) (t +2) = 0

so t = 3 or t = -2

Answer 2

I assume you want to find t
you have t^2 + t - 6 = 2t

make the right side 0 by subtracting 2t from both sides.
then you have

t^2 - t - 6 = 0

factor it...

(t-3) (t+2) = 0

you know what? t-3 = 0 or t+2 = 0

then solve for t!

Answer 3

t² + t - 6 = 2t

t² + t - 6 - t = 2t - t

t² - 6 = t

t² - 6 - t = t - t

t² - t - 6 = 0

(t - 3)(t + 2)

(t - 3)(t + 2) = t² - 3t + 2t - 6 = t² - t - 6

The answer is x = 3 and x = - 2

Insert the x value into the equation

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Check

x = 3

t² + t - 6 = 2t

(3)² + 3 - 6 = 2(3)

9 + 3 - 6 = 6

12 - 6 = 6

6 = 6
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Check

x = - 2

t² + t - 6 = 2t

(- 2)² + (- 2) - 6 = 2(- 2)

4 - 2 - 6 = - 4

4 - 8 = - 4

- 4 = - 4
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Roots

t = 3

t = - 2

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Answer 4

t² - t - 6 = 0

now factor it to:

(t + 2)*(t - 3) = 0

one or both of the expressions in parenthesis must be zero to make the entire expression true so:
(t + 2) = 0 and/or (t - 3) = 0
t = -2 and/or t = 3

so t = -2 and/or 3

Answer 5

hmm, thats only one variable, t, right? If so, subtract 2t from both sides.

t² - t - 6 = 0

Then factor.

(t - 3)(t + 2)=0

That means t can either equal 3 or -2.

Answer 6

t^2 + t - 6 = 2t
t^2 - 6 = t
t^2 = t + 6
t = sqrt(t + 6)

Answer 7

if a/b=c/d, then ad=bc here, x^2+2x=15 so x^2+2x-15=0 (x-3)(x+5)=0 then,x=3 & x=-5 God bless you.