2x^2-5x+6=3x-2

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Solution for 2x^2-5x+6=3x-2 equation: 


Simplifying
2x2 + -5x + 6 = 3x + -2

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

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

Solving
6 + -5x + 2x2 = -2 + 3x

Solving for variable 'x'.

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

Combine like terms: 6 + 2 = 8
8 + -5x + -3x + 2x2 = -2 + 3x + 2 + -3x

Combine like terms: -5x + -3x = -8x
8 + -8x + 2x2 = -2 + 3x + 2 + -3x

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

Combine like terms: -2 + 2 = 0
8 + -8x + 2x2 = 0 + 3x + -3x
8 + -8x + 2x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
8 + -8x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(4 + -4x + x2) = 0

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

Ignore the factor 2.

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 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 + -1x = 0 + -2

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

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

Divide each side by '-1'.
x = 2

Simplifying
x = 2

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 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 + -1x = 0 + -2

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

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

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {2, 2}

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