2x(1-3x)-1+3x=0

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Solution for 2x(1-3x)-1+3x=0 equation:


Simplifying
2x(1 + -3x) + -1 + 3x = 0
(1 * 2x + -3x * 2x) + -1 + 3x = 0
(2x + -6x2) + -1 + 3x = 0

Reorder the terms:
-1 + 2x + 3x + -6x2 = 0

Combine like terms: 2x + 3x = 5x
-1 + 5x + -6x2 = 0

Solving
-1 + 5x + -6x2 = 0

Solving for variable 'x'.

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

Subproblem 1

Set the factor '(-1 + 2x)' equal to zero and attempt to solve: Simplifying -1 + 2x = 0 Solving -1 + 2x = 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 + 2x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 2x = 0 + 1 2x = 0 + 1 Combine like terms: 0 + 1 = 1 2x = 1 Divide each side by '2'. x = 0.5 Simplifying x = 0.5

Subproblem 2

Set the factor '(1 + -3x)' equal to zero and attempt to solve: Simplifying 1 + -3x = 0 Solving 1 + -3x = 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 + -3x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3x = 0 + -1 -3x = 0 + -1 Combine like terms: 0 + -1 = -1 -3x = -1 Divide each side by '-3'. x = 0.3333333333 Simplifying x = 0.3333333333

Solution

x = {0.5, 0.3333333333}

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