2X^2+5X=2X+9

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Solution for 2X^2+5X=2X+9 equation: 


Simplifying
2X2 + 5X = 2X + 9

Reorder the terms:
5X + 2X2 = 2X + 9

Reorder the terms:
5X + 2X2 = 9 + 2X

Solving
5X + 2X2 = 9 + 2X

Solving for variable 'X'.

Reorder the terms:
-9 + 5X + -2X + 2X2 = 9 + 2X + -9 + -2X

Combine like terms: 5X + -2X = 3X
-9 + 3X + 2X2 = 9 + 2X + -9 + -2X

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

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

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

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


Subproblem 1
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

Subproblem 2
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
Solution
X = {-3, 1.5}

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