2X^2-3X=9

Solution for 2X^2-3X=9 equation:

Simplifying
2X2 + -3X = 9

Reorder the terms:
-3X + 2X2 = 9

Solving
-3X + 2X2 = 9

Solving for variable 'X'.

Reorder the terms:
-9 + -3X + 2X2 = 9 + -9

Combine like terms: 9 + -9 = 0
-9 + -3X + 2X2 = 0

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

Subproblem 1
Set the factor '(-3 + -2X)' equal to zero and attempt to solve:

Simplifying
-3 + -2X = 0

Solving
-3 + -2X = 0

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

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

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

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

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

Simplifying
X = -1.5
Subproblem 2
Set the factor '(3 + -1X)' equal to zero and attempt to solve:

Simplifying
3 + -1X = 0

Solving
3 + -1X = 0

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

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

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

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

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

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