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Simplifying 6t5 + 3t4 = -12t3 Reorder the terms: 3t4 + 6t5 = -12t3 Solving 3t4 + 6t5 = -12t3 Solving for variable 't'. Reorder the terms: 12t3 + 3t4 + 6t5 = -12t3 + 12t3 Combine like terms: -12t3 + 12t3 = 0 12t3 + 3t4 + 6t5 = 0 Factor out the Greatest Common Factor (GCF), '3t3'. 3t3(4 + t + 2t2) = 0 Ignore the factor 3.Subproblem 1
Set the factor 't3' equal to zero and attempt to solve: Simplifying t3 = 0 Solving t3 = 0 Move all terms containing t to the left, all other terms to the right. Simplifying t3 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(4 + t + 2t2)' equal to zero and attempt to solve: Simplifying 4 + t + 2t2 = 0 Solving 4 + t + 2t2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 2 + 0.5t + t2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + 0.5t + -2 + t2 = 0 + -2 Reorder the terms: 2 + -2 + 0.5t + t2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 0.5t + t2 = 0 + -2 0.5t + t2 = 0 + -2 Combine like terms: 0 + -2 = -2 0.5t + t2 = -2 The t term is t. 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. 0.5t + 0.25 + t2 = -2 + 0.25 Reorder the terms: 0.25 + 0.5t + t2 = -2 + 0.25 Combine like terms: -2 + 0.25 = -1.75 0.25 + 0.5t + t2 = -1.75 Factor a perfect square on the left side: (t + 0.5)(t + 0.5) = -1.75 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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