12n^2+12=3n

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Solution for 12n^2+12=3n equation:


Simplifying
12n2 + 12 = 3n

Reorder the terms:
12 + 12n2 = 3n

Solving
12 + 12n2 = 3n

Solving for variable 'n'.

Reorder the terms:
12 + -3n + 12n2 = 3n + -3n

Combine like terms: 3n + -3n = 0
12 + -3n + 12n2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(4 + -1n + 4n2) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(4 + -1n + 4n2)' equal to zero and attempt to solve: Simplifying 4 + -1n + 4n2 = 0 Solving 4 + -1n + 4n2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1 + -0.25n + n2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -0.25n + -1 + n2 = 0 + -1 Reorder the terms: 1 + -1 + -0.25n + n2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -0.25n + n2 = 0 + -1 -0.25n + n2 = 0 + -1 Combine like terms: 0 + -1 = -1 -0.25n + n2 = -1 The n term is -0.25n. Take half its coefficient (-0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. -0.25n + 0.015625 + n2 = -1 + 0.015625 Reorder the terms: 0.015625 + -0.25n + n2 = -1 + 0.015625 Combine like terms: -1 + 0.015625 = -0.984375 0.015625 + -0.25n + n2 = -0.984375 Factor a perfect square on the left side: (n + -0.125)(n + -0.125) = -0.984375 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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