x(3x+1)=2

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


Simplifying
x(3x + 1) = 2

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

Solving
1x + 3x2 = 2

Solving for variable 'x'.

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

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

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

Subproblem 1

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

Subproblem 2

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

Solution

x = {-1, 0.6666666667}

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