x^2+5x-3=7x-3

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Solution for x^2+5x-3=7x-3 equation: 


Simplifying
x2 + 5x + -3 = 7x + -3

Reorder the terms:
-3 + 5x + x2 = 7x + -3

Reorder the terms:
-3 + 5x + x2 = -3 + 7x

Add '3' to each side of the equation.
-3 + 5x + 3 + x2 = -3 + 3 + 7x

Reorder the terms:
-3 + 3 + 5x + x2 = -3 + 3 + 7x

Combine like terms: -3 + 3 = 0
0 + 5x + x2 = -3 + 3 + 7x
5x + x2 = -3 + 3 + 7x

Combine like terms: -3 + 3 = 0
5x + x2 = 0 + 7x
5x + x2 = 7x

Solving
5x + x2 = 7x

Solving for variable 'x'.

Reorder the terms:
5x + -7x + x2 = 7x + -7x

Combine like terms: 5x + -7x = -2x
-2x + x2 = 7x + -7x

Combine like terms: 7x + -7x = 0
-2x + x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-2 + 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 '(-2 + x)' equal to zero and attempt to solve:

Simplifying
-2 + x = 0

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

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

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

Simplifying
x = 2
Solution
x = {0, 2}

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