Given the quadratic equation:

u^2 + 6u = 27

We need to solve for u.

First we will rewrite into the standard form.

==> u^2 + 6u - 27 = 0

Now we will factor the equation.

==> (u+9)(u-3) = 0

Now we will solve.

==> u1= -9 and u2= 3

Then, we have two solutions for the quadratic equations.

**==> -9 and 3 are the roots for the equation.**

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We have to solve the equation u^2 + 6u = 27.

First bring all the terms to one side

=> u^2 + 6u - 27 = 0

One method of finding the roots which works when the roots are integers or fractions is to split the coefficient of u into two parts which add up to 6 and the product of which is -27. We can achieve this with 9 and -3.

=> u^2 + 9u - 3u - 27 = 0

remove the common factors of the first two terms and the last two terms.

=> u(u + 9) - 3(u + 9)

factorize again

=>(u - 3)(u + 9) = 0

u - 3 = 0 => u = 3

and u + 9 = 0 => u = -9

**This gives us the roots of the equation as 3 and -9.**

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