5x^2-3x=3x-1

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Solution for 5x^2-3x=3x-1 equation: 


Simplifying
5x2 + -3x = 3x + -1

Reorder the terms:
-3x + 5x2 = 3x + -1

Reorder the terms:
-3x + 5x2 = -1 + 3x

Solving
-3x + 5x2 = -1 + 3x

Solving for variable 'x'.

Reorder the terms:
1 + -3x + -3x + 5x2 = -1 + 3x + 1 + -3x

Combine like terms: -3x + -3x = -6x
1 + -6x + 5x2 = -1 + 3x + 1 + -3x

Reorder the terms:
1 + -6x + 5x2 = -1 + 1 + 3x + -3x

Combine like terms: -1 + 1 = 0
1 + -6x + 5x2 = 0 + 3x + -3x
1 + -6x + 5x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
1 + -6x + 5x2 = 0

Factor a trinomial.
(1 + -5x)(1 + -1x) = 0


Subproblem 1
Set the factor '(1 + -5x)' equal to zero and attempt to solve:

Simplifying
1 + -5x = 0

Solving
1 + -5x = 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 + -5x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -5x = 0 + -1
-5x = 0 + -1

Combine like terms: 0 + -1 = -1
-5x = -1

Divide each side by '-5'.
x = 0.2

Simplifying
x = 0.2

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

Simplifying
1 + -1x = 0

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

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

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

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

Simplifying
x = 1
Solution
x = {0.2, 1}

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