5t^3+12t^2+14t=0

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Solution for 5t^3+12t^2+14t=0 equation:


Simplifying
5t3 + 12t2 + 14t = 0

Reorder the terms:
14t + 12t2 + 5t3 = 0

Solving
14t + 12t2 + 5t3 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), 't'.
t(14 + 12t + 5t2) = 0

Subproblem 1

Set the factor 't' equal to zero and attempt to solve: Simplifying t = 0 Solving t = 0 Move all terms containing t to the left, all other terms to the right. Simplifying t = 0

Subproblem 2

Set the factor '(14 + 12t + 5t2)' equal to zero and attempt to solve: Simplifying 14 + 12t + 5t2 = 0 Solving 14 + 12t + 5t2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 2.8 + 2.4t + t2 = 0 Move the constant term to the right: Add '-2.8' to each side of the equation. 2.8 + 2.4t + -2.8 + t2 = 0 + -2.8 Reorder the terms: 2.8 + -2.8 + 2.4t + t2 = 0 + -2.8 Combine like terms: 2.8 + -2.8 = 0.0 0.0 + 2.4t + t2 = 0 + -2.8 2.4t + t2 = 0 + -2.8 Combine like terms: 0 + -2.8 = -2.8 2.4t + t2 = -2.8 The t term is 2.4t. Take half its coefficient (1.2). Square it (1.44) and add it to both sides. Add '1.44' to each side of the equation. 2.4t + 1.44 + t2 = -2.8 + 1.44 Reorder the terms: 1.44 + 2.4t + t2 = -2.8 + 1.44 Combine like terms: -2.8 + 1.44 = -1.36 1.44 + 2.4t + t2 = -1.36 Factor a perfect square on the left side: (t + 1.2)(t + 1.2) = -1.36 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.

Solution

t = {0}

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