2x^2+6x=3x+9

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Solution for 2x^2+6x=3x+9 equation: 


Simplifying
2x2 + 6x = 3x + 9

Reorder the terms:
6x + 2x2 = 3x + 9

Reorder the terms:
6x + 2x2 = 9 + 3x

Solving
6x + 2x2 = 9 + 3x

Solving for variable 'x'.

Reorder the terms:
-9 + 6x + -3x + 2x2 = 9 + 3x + -9 + -3x

Combine like terms: 6x + -3x = 3x
-9 + 3x + 2x2 = 9 + 3x + -9 + -3x

Reorder the terms:
-9 + 3x + 2x2 = 9 + -9 + 3x + -3x

Combine like terms: 9 + -9 = 0
-9 + 3x + 2x2 = 0 + 3x + -3x
-9 + 3x + 2x2 = 3x + -3x

Combine like terms: 3x + -3x = 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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