x(3x-1)-(3-x)=3x-5x+2

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Solution for x(3x-1)-(3-x)=3x-5x+2 equation:


Simplifying
x(3x + -1) + -1(3 + -1x) = 3x + -5x + 2

Reorder the terms:
x(-1 + 3x) + -1(3 + -1x) = 3x + -5x + 2
(-1 * x + 3x * x) + -1(3 + -1x) = 3x + -5x + 2
(-1x + 3x2) + -1(3 + -1x) = 3x + -5x + 2
-1x + 3x2 + (3 * -1 + -1x * -1) = 3x + -5x + 2
-1x + 3x2 + (-3 + 1x) = 3x + -5x + 2

Reorder the terms:
-3 + -1x + 1x + 3x2 = 3x + -5x + 2

Combine like terms: -1x + 1x = 0
-3 + 0 + 3x2 = 3x + -5x + 2
-3 + 3x2 = 3x + -5x + 2

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

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

Solving
-3 + 3x2 = 2 + -2x

Solving for variable 'x'.

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

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

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

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

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

Factor a trinomial.
(-5 + -3x)(1 + -1x) = 0


Subproblem 1
Set the factor '(-5 + -3x)' equal to zero and attempt to solve:

Simplifying
-5 + -3x = 0

Solving
-5 + -3x = 0

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

Add '5' to each side of the equation.
-5 + 5 + -3x = 0 + 5

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

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

Divide each side by '-3'.
x = -1.666666667

Simplifying
x = -1.666666667

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 = {-1.666666667, 1}

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