-2x=3x^2-1

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


Simplifying
-2x = 3x2 + -1

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

Solving
-2x = -1 + 3x2

Solving for variable 'x'.

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

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

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

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

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

Subproblem 1

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

Subproblem 2

Set the factor '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 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 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Simplifying x = -1

Solution

x = {0.3333333333, -1}

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