3x^2+2x=12x+8

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Solution for 3x^2+2x=12x+8 equation: 


Simplifying
3x2 + 2x = 12x + 8

Reorder the terms:
2x + 3x2 = 12x + 8

Reorder the terms:
2x + 3x2 = 8 + 12x

Solving
2x + 3x2 = 8 + 12x

Solving for variable 'x'.

Reorder the terms:
-8 + 2x + -12x + 3x2 = 8 + 12x + -8 + -12x

Combine like terms: 2x + -12x = -10x
-8 + -10x + 3x2 = 8 + 12x + -8 + -12x

Reorder the terms:
-8 + -10x + 3x2 = 8 + -8 + 12x + -12x

Combine like terms: 8 + -8 = 0
-8 + -10x + 3x2 = 0 + 12x + -12x
-8 + -10x + 3x2 = 12x + -12x

Combine like terms: 12x + -12x = 0
-8 + -10x + 3x2 = 0

Factor a trinomial.
(-2 + -3x)(4 + -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 '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-0.6666666667, 4}

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