3X^2-9X+2=4X+12

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Solution for 3X^2-9X+2=4X+12 equation: 


Simplifying
3X2 + -9X + 2 = 4X + 12

Reorder the terms:
2 + -9X + 3X2 = 4X + 12

Reorder the terms:
2 + -9X + 3X2 = 12 + 4X

Solving
2 + -9X + 3X2 = 12 + 4X

Solving for variable 'X'.

Reorder the terms:
2 + -12 + -9X + -4X + 3X2 = 12 + 4X + -12 + -4X

Combine like terms: 2 + -12 = -10
-10 + -9X + -4X + 3X2 = 12 + 4X + -12 + -4X

Combine like terms: -9X + -4X = -13X
-10 + -13X + 3X2 = 12 + 4X + -12 + -4X

Reorder the terms:
-10 + -13X + 3X2 = 12 + -12 + 4X + -4X

Combine like terms: 12 + -12 = 0
-10 + -13X + 3X2 = 0 + 4X + -4X
-10 + -13X + 3X2 = 4X + -4X

Combine like terms: 4X + -4X = 0
-10 + -13X + 3X2 = 0

Factor a trinomial.
(-2 + -3X)(5 + -1X) = 0


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

Simplifying
-2 + -3X = 0

Solving
-2 + -3X = 0

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

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

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

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

Divide each side by '-3'.
X = -0.6666666667

Simplifying
X = -0.6666666667

Subproblem 2
Set the factor '(5 + -1X)' equal to zero and attempt to solve:

Simplifying
5 + -1X = 0

Solving
5 + -1X = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1X = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1X = 0 + -5
-1X = 0 + -5

Combine like terms: 0 + -5 = -5
-1X = -5

Divide each side by '-1'.
X = 5

Simplifying
X = 5
Solution
X = {-0.6666666667, 5}

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