Solve 16t^4-24t^3-8t^212t

Question

Simplify the expression

16 t^{4} - 120 t^{3}

Evaluate

16 t^{4} - 24 t^{3} - 8 t^{2} \times 12 t

Multiply

More Steps

Multiply the terms

- 8 t^{2} \times 12 t

Multiply the terms

- 96 t^{2} \times t

Multiply the terms with the same base by adding their exponents

- 96 t^{2 + 1}

Add the numbers

- 96 t^{3}

16 t^{4} - 24 t^{3} - 96 t^{3}

Solution

More Steps

Evaluate

- 24 t^{3} - 96 t^{3}

Collect like terms by calculating the sum or difference of their coefficients

(- 24 - 96) t^{3}

Subtract the numbers

- 120 t^{3}

16 t^{4} - 120 t^{3}

Show Solution

Factor the expression

8 t^{3} (2 t - 15)

Evaluate

16 t^{4} - 24 t^{3} - 8 t^{2} \times 12 t

Multiply

More Steps

Multiply the terms

8 t^{2} \times 12 t

Multiply the terms

96 t^{2} \times t

Multiply the terms with the same base by adding their exponents

96 t^{2 + 1}

Add the numbers

96 t^{3}

16 t^{4} - 24 t^{3} - 96 t^{3}

Subtract the terms

More Steps

Evaluate

- 24 t^{3} - 96 t^{3}

Collect like terms by calculating the sum or difference of their coefficients

(- 24 - 96) t^{3}

Subtract the numbers

- 120 t^{3}

16 t^{4} - 120 t^{3}

Rewrite the expression

8 t^{3} \times 2 t - 8 t^{3} \times 15

Solution

8 t^{3} (2 t - 15)

Show Solution

Find the roots

t_{1} = 0, t_{2} = \frac{15}{2}

Alternative Form

t_{1} = 0, t_{2} = 7.5

Evaluate

16 t^{4} - 24 t^{3} - 8 t^{2} \times 12 t

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

16 t^{4} - 24 t^{3} - 8 t^{2} \times 12 t = 0

Multiply

More Steps

Multiply the terms

8 t^{2} \times 12 t

Multiply the terms

96 t^{2} \times t

Multiply the terms with the same base by adding their exponents

96 t^{2 + 1}

Add the numbers

96 t^{3}

16 t^{4} - 24 t^{3} - 96 t^{3} = 0

Subtract the terms

More Steps

Simplify

16 t^{4} - 24 t^{3} - 96 t^{3}

Subtract the terms

More Steps

Evaluate

- 24 t^{3} - 96 t^{3}

Collect like terms by calculating the sum or difference of their coefficients

(- 24 - 96) t^{3}

Subtract the numbers

- 120 t^{3}

16 t^{4} - 120 t^{3}

16 t^{4} - 120 t^{3} = 0

Factor the expression

8 t^{3} (2 t - 15) = 0

Divide both sides

t^{3} (2 t - 15) = 0

Separate the equation into 2 possible cases

t^{3} = 0 2 t - 15 = 0

The only way a power can be 0 is when the base equals 0

t = 0 2 t - 15 = 0

Solve the equation

More Steps

Evaluate

2 t - 15 = 0

Move the constant to the right-hand side and change its sign

2 t = 0 + 15

Removing 0 doesn't change the value,so remove it from the expression

2 t = 15

Divide both sides

\frac{2 t}{2} = \frac{15}{2}

Divide the numbers

t = \frac{15}{2}

t = 0 t = \frac{15}{2}

Solution

t_{1} = 0, t_{2} = \frac{15}{2}

Alternative Form

t_{1} = 0, t_{2} = 7.5

Show Solution