0=-x^2+3x

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Solution for 0=-x^2+3x equation: 


Simplifying
0 = -1x2 + 3x

Reorder the terms:
0 = 3x + -1x2

Solving
0 = 3x + -1x2

Solving for variable 'x'.
Remove the zero:
-3x + x2 = 3x + -1x2 + -3x + x2

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

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

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

Factor out the Greatest Common Factor (GCF), 'x'.
x(-3 + x) = 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 '(-3 + x)' equal to zero and attempt to solve:

Simplifying
-3 + x = 0

Solving
-3 + x = 0

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

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

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

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

Simplifying
x = 3
Solution
x = {0, 3}

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