Solve 3040(t^2 4t) - 3(4t^2 2024t 8096)

Question

Simplify the expression

- 196623488 t^{3}

Evaluate

3040 (t^{2} \times 4 t) - 3 (4 t^{2} \times 2024 t \times 8096)

Remove the parentheses

3040 t^{2} \times 4 t - 3 \times 4 t^{2} \times 2024 t \times 8096

Multiply

More Steps

Multiply the terms

3040 t^{2} \times 4 t

Multiply the terms

12160 t^{2} \times t

Multiply the terms with the same base by adding their exponents

12160 t^{2 + 1}

Add the numbers

12160 t^{3}

12160 t^{3} - 3 \times 4 t^{2} \times 2024 t \times 8096

Multiply

More Steps

Multiply the terms

3 \times 4 t^{2} \times 2024 t \times 8096

Multiply the terms

More Steps

Evaluate

3 \times 4 \times 2024 \times 8096

Multiply the terms

12 \times 2024 \times 8096

Multiply the terms

24288 \times 8096

Multiply the numbers

196635648

196635648 t^{2} \times t

Multiply the terms with the same base by adding their exponents

196635648 t^{2 + 1}

Add the numbers

196635648 t^{3}

12160 t^{3} - 196635648 t^{3}

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

(12160 - 196635648) t^{3}

Solution

- 196623488 t^{3}

Show Solution

Find the roots

t = 0

Evaluate

3040 (t^{2} \times 4 t) - 3 (4 t^{2} \times 2024 t \times 8096)

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

3040 (t^{2} \times 4 t) - 3 (4 t^{2} \times 2024 t \times 8096) = 0

Multiply

More Steps

Multiply the terms

t^{2} \times 4 t

Multiply the terms with the same base by adding their exponents

t^{2 + 1} \times 4

Add the numbers

t^{3} \times 4

Use the commutative property to reorder the terms

4 t^{3}

3040 \times 4 t^{3} - 3 (4 t^{2} \times 2024 t \times 8096) = 0

Multiply

More Steps

Multiply the terms

4 t^{2} \times 2024 t \times 8096

Multiply the terms

More Steps

Evaluate

4 \times 2024 \times 8096

Multiply the terms

8096 \times 8096

Multiply the numbers

65545216

65545216 t^{2} \times t

Multiply the terms with the same base by adding their exponents

65545216 t^{2 + 1}

Add the numbers

65545216 t^{3}

3040 \times 4 t^{3} - 3 \times 65545216 t^{3} = 0

Multiply the numbers

12160 t^{3} - 3 \times 65545216 t^{3} = 0

Multiply the numbers

12160 t^{3} - 196635648 t^{3} = 0

Subtract the terms

More Steps

Simplify

12160 t^{3} - 196635648 t^{3}

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

(12160 - 196635648) t^{3}

Subtract the numbers

- 196623488 t^{3}

- 196623488 t^{3} = 0

Change the signs on both sides of the equation

196623488 t^{3} = 0

Rewrite the expression

t^{3} = 0

Solution

t = 0

Show Solution