2u^2+3u-9=0

Solution for 2u^2+3u-9=0 equation:

Simplifying
2u2 + 3u + -9 = 0

Reorder the terms:
-9 + 3u + 2u2 = 0

Solving
-9 + 3u + 2u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(-3 + -1u)(3 + -2u) = 0

Subproblem 1
Set the factor '(-3 + -1u)' equal to zero and attempt to solve:

Simplifying
-3 + -1u = 0

Solving
-3 + -1u = 0

Move all terms containing u to the left, all other terms to the right.

Add '3' to each side of the equation.
-3 + 3 + -1u = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1u = 0 + 3
-1u = 0 + 3

Combine like terms: 0 + 3 = 3
-1u = 3

Divide each side by '-1'.
u = -3

Simplifying
u = -3
Subproblem 2
Set the factor '(3 + -2u)' equal to zero and attempt to solve:

Simplifying
3 + -2u = 0

Solving
3 + -2u = 0

Move all terms containing u to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + -2u = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2u = 0 + -3
-2u = 0 + -3

Combine like terms: 0 + -3 = -3
-2u = -3

Divide each side by '-2'.
u = 1.5

Simplifying
u = 1.5
Solution
u = {-3, 1.5}