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

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


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

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

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

Remove parenthesis around (2x)
-1x + 3x2 + -1 * 2x = 3x + -5x + 2

Multiply -1 * 2
-1x + 3x2 + -2x = 3x + -5x + 2

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

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

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

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

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

Solving for variable 'x'.

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

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

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

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

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

Factor a trinomial.
(-2 + -3x)(1 + -1x) = 0

Subproblem 1

Set the factor '(-2 + -3x)' equal to zero and attempt to solve: Simplifying -2 + -3x = 0 Solving -2 + -3x = 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 + -3x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -3x = 0 + 2 -3x = 0 + 2 Combine like terms: 0 + 2 = 2 -3x = 2 Divide each side by '-3'. x = -0.6666666667 Simplifying x = -0.6666666667

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 = {-0.6666666667, 1}

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