Solve 6(3t^2 t 1) - 2t(3 - 4t)

Question

Simplify the expression

18 t^{3} - 6 t + 8 t^{2}

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2 t (9 t^{2} - 3 + 4 t)

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t_{1} = - \frac{2 + 31}{9}, t_{2} = 0, t_{3} = \frac{- 2 + 31}{9}

Alternative Form

t_{1} \approx - 0.840863, t_{2} = 0, t_{3} \approx 0.396418

Evaluate

6 (3 t^{2} \times t \times 1) - 2 t (3 - 4 t)

To find the roots of the expression,set the expression equal to 0

6 (3 t^{2} \times t \times 1) - 2 t (3 - 4 t) = 0

Multiply the terms

More Steps

6 \times 3 t^{3} - 2 t (3 - 4 t) = 0

Multiply the numbers

18 t^{3} - 2 t (3 - 4 t) = 0

Calculate

More Steps

18 t^{3} - 6 t + 8 t^{2} = 0

Factor the expression

2 t (9 t^{2} - 3 + 4 t) = 0

Divide both sides

t (9 t^{2} - 3 + 4 t) = 0

Separate the equation into 2 possible cases

t = 0 9 t^{2} - 3 + 4 t = 0

Solve the equation

More Steps

t = 0 t = \frac{- 2 + 31}{9} t = - \frac{2 + 31}{9}

Solution

t_{1} = - \frac{2 + 31}{9}, t_{2} = 0, t_{3} = \frac{- 2 + 31}{9}

Alternative Form

t_{1} \approx - 0.840863, t_{2} = 0, t_{3} \approx 0.396418

Show Solution