54=3x^2-x+2

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Solution for 54=3x^2-x+2 equation:


Simplifying
54 = 3x2 + -1x + 2

Reorder the terms:
54 = 2 + -1x + 3x2

Solving
54 = 2 + -1x + 3x2

Solving for variable 'x'.

Combine like terms: 54 + -2 = 52
52 + x + -3x2 = 2 + -1x + 3x2 + -2 + x + -3x2

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

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

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

Combine like terms: 3x2 + -3x2 = 0
52 + x + -3x2 = 0

Factor a trinomial.
(13 + -3x)(4 + x) = 0

Subproblem 1

Set the factor '(13 + -3x)' equal to zero and attempt to solve: Simplifying 13 + -3x = 0 Solving 13 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + -3x = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -3x = 0 + -13 -3x = 0 + -13 Combine like terms: 0 + -13 = -13 -3x = -13 Divide each side by '-3'. x = 4.333333333 Simplifying x = 4.333333333

Subproblem 2

Set the factor '(4 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 x = -4 Simplifying x = -4

Solution

x = {4.333333333, -4}

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