6x^2-2x+3=3x+2

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


Simplifying
6x2 + -2x + 3 = 3x + 2

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

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

Solving
3 + -2x + 6x2 = 2 + 3x

Solving for variable 'x'.

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

Combine like terms: 3 + -2 = 1
1 + -2x + -3x + 6x2 = 2 + 3x + -2 + -3x

Combine like terms: -2x + -3x = -5x
1 + -5x + 6x2 = 2 + 3x + -2 + -3x

Reorder the terms:
1 + -5x + 6x2 = 2 + -2 + 3x + -3x

Combine like terms: 2 + -2 = 0
1 + -5x + 6x2 = 0 + 3x + -3x
1 + -5x + 6x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
1 + -5x + 6x2 = 0

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


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

Simplifying
1 + -3x = 0

Solving
1 + -3x = 0

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

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

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

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

Divide each side by '-3'.
x = 0.3333333333

Simplifying
x = 0.3333333333

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

Simplifying
1 + -2x = 0

Solving
1 + -2x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2x = 0 + -1
-2x = 0 + -1

Combine like terms: 0 + -1 = -1
-2x = -1

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5
Solution
x = {0.3333333333, 0.5}

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