Solve 6t^4-12t^3-54t^2 108t

Question

Simplify the expression

6 t^{4} - 5844 t^{3}

Evaluate

6 t^{4} - 12 t^{3} - 54 t^{2} \times 108 t

Multiply

More Steps

Multiply the terms

- 54 t^{2} \times 108 t

Multiply the terms

- 5832 t^{2} \times t

Multiply the terms with the same base by adding their exponents

- 5832 t^{2 + 1}

Add the numbers

- 5832 t^{3}

6 t^{4} - 12 t^{3} - 5832 t^{3}

Solution

More Steps

Evaluate

- 12 t^{3} - 5832 t^{3}

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

(- 12 - 5832) t^{3}

Subtract the numbers

- 5844 t^{3}

6 t^{4} - 5844 t^{3}

Show Solution

Factor the expression

6 t^{3} (t - 974)

Evaluate

6 t^{4} - 12 t^{3} - 54 t^{2} \times 108 t

Multiply

More Steps

Multiply the terms

54 t^{2} \times 108 t

Multiply the terms

5832 t^{2} \times t

Multiply the terms with the same base by adding their exponents

5832 t^{2 + 1}

Add the numbers

5832 t^{3}

6 t^{4} - 12 t^{3} - 5832 t^{3}

Subtract the terms

More Steps

Evaluate

- 12 t^{3} - 5832 t^{3}

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

(- 12 - 5832) t^{3}

Subtract the numbers

- 5844 t^{3}

6 t^{4} - 5844 t^{3}

Rewrite the expression

6 t^{3} \times t - 6 t^{3} \times 974

Solution

6 t^{3} (t - 974)

Show Solution

Find the roots

t_{1} = 0, t_{2} = 974

Evaluate

6 t^{4} - 12 t^{3} - 54 t^{2} \times 108 t

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

6 t^{4} - 12 t^{3} - 54 t^{2} \times 108 t = 0

Multiply

More Steps

Multiply the terms

54 t^{2} \times 108 t

Multiply the terms

5832 t^{2} \times t

Multiply the terms with the same base by adding their exponents

5832 t^{2 + 1}

Add the numbers

5832 t^{3}

6 t^{4} - 12 t^{3} - 5832 t^{3} = 0

Subtract the terms

More Steps

Simplify

6 t^{4} - 12 t^{3} - 5832 t^{3}

Subtract the terms

More Steps

Evaluate

- 12 t^{3} - 5832 t^{3}

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

(- 12 - 5832) t^{3}

Subtract the numbers

- 5844 t^{3}

6 t^{4} - 5844 t^{3}

6 t^{4} - 5844 t^{3} = 0

Factor the expression

6 t^{3} (t - 974) = 0

Divide both sides

t^{3} (t - 974) = 0

Separate the equation into 2 possible cases

t^{3} = 0 t - 974 = 0

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

t = 0 t - 974 = 0

Solve the equation

More Steps

Evaluate

t - 974 = 0

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

t = 0 + 974

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

t = 974

t = 0 t = 974

Solution

t_{1} = 0, t_{2} = 974

Show Solution