3x^2-4x=x^2-3x

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Solution for 3x^2-4x=x^2-3x equation: 


Simplifying
3x2 + -4x = x2 + -3x

Reorder the terms:
-4x + 3x2 = x2 + -3x

Reorder the terms:
-4x + 3x2 = -3x + x2

Solving
-4x + 3x2 = -3x + x2

Solving for variable 'x'.

Reorder the terms:
-4x + 3x + 3x2 + -1x2 = -3x + x2 + 3x + -1x2

Combine like terms: -4x + 3x = -1x
-1x + 3x2 + -1x2 = -3x + x2 + 3x + -1x2

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

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

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

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

Factor out the Greatest Common Factor (GCF), 'x'.
x(-1 + 2x) = 0


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

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, 0.5}

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