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

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


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

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

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

Add '-3' to each side of the equation.
3 + -3x + -3 + 5x2 = 3 + -3 + 2x2

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

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

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

Solving
-3x + 5x2 = 2x2

Solving for variable 'x'.

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

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

Factor out the Greatest Common Factor (GCF), '3x'.
3x(-1 + x) = 0

Ignore the factor 3.

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 + x)' equal to zero and attempt to solve: Simplifying -1 + x = 0 Solving -1 + x = 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 + x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + x = 0 + 1 x = 0 + 1 Combine like terms: 0 + 1 = 1 x = 1 Simplifying x = 1

Solution

x = {0, 1}

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