3x-6x^2=24

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Solution for 3x-6x^2=24 equation:


Simplifying
3x + -6x2 = 24

Solving
3x + -6x2 = 24

Solving for variable 'x'.

Reorder the terms:
-24 + 3x + -6x2 = 24 + -24

Combine like terms: 24 + -24 = 0
-24 + 3x + -6x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-8 + x + -2x2) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(-8 + x + -2x2)' equal to zero and attempt to solve: Simplifying -8 + x + -2x2 = 0 Solving -8 + x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 4 + -0.5x + x2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + -0.5x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + -0.5x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -0.5x + x2 = 0 + -4 -0.5x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 -0.5x + x2 = -4 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -0.5x + 0.25 + x2 = -4 + 0.25 Reorder the terms: 0.25 + -0.5x + x2 = -4 + 0.25 Combine like terms: -4 + 0.25 = -3.75 0.25 + -0.5x + x2 = -3.75 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -3.75 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.

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