3v^2+12v-6=-24

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Solution for 3v^2+12v-6=-24 equation:


Simplifying
3v2 + 12v + -6 = -24

Reorder the terms:
-6 + 12v + 3v2 = -24

Solving
-6 + 12v + 3v2 = -24

Solving for variable 'v'.

Reorder the terms:
-6 + 24 + 12v + 3v2 = -24 + 24

Combine like terms: -6 + 24 = 18
18 + 12v + 3v2 = -24 + 24

Combine like terms: -24 + 24 = 0
18 + 12v + 3v2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(6 + 4v + v2) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(6 + 4v + v2)' equal to zero and attempt to solve: Simplifying 6 + 4v + v2 = 0 Solving 6 + 4v + v2 = 0 Begin completing the square. Move the constant term to the right: Add '-6' to each side of the equation. 6 + 4v + -6 + v2 = 0 + -6 Reorder the terms: 6 + -6 + 4v + v2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + 4v + v2 = 0 + -6 4v + v2 = 0 + -6 Combine like terms: 0 + -6 = -6 4v + v2 = -6 The v term is 4v. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4v + 4 + v2 = -6 + 4 Reorder the terms: 4 + 4v + v2 = -6 + 4 Combine like terms: -6 + 4 = -2 4 + 4v + v2 = -2 Factor a perfect square on the left side: (v + 2)(v + 2) = -2 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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