3x^2+1=-4x

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Solution for 3x^2+1=-4x equation:


Simplifying
3x2 + 1 = -4x

Reorder the terms:
1 + 3x2 = -4x

Solving
1 + 3x2 = -4x

Solving for variable 'x'.

Reorder the terms:
1 + 4x + 3x2 = -4x + 4x

Combine like terms: -4x + 4x = 0
1 + 4x + 3x2 = 0

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

Subproblem 1

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

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 = {-1, -0.3333333333}

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