Solve (t -2 t^2 )(2 t - 3 t )

Question

Simplify the expression

- t^{2} + 2 t^{3}

Evaluate

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

Subtract the terms

More Steps

Simplify

2 t - 3 t

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

(2 - 3) t

Subtract the numbers

- t

(t - 2 t^{2}) (- t)

Multiply the terms

- t (t - 2 t^{2})

Apply the distributive property

- t \times t - (- t \times 2 t^{2})

Multiply the terms

- t^{2} - (- t \times 2 t^{2})

Multiply the terms

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Evaluate

- t \times 2 t^{2}

Multiply the numbers

- 2 t \times t^{2}

Multiply the terms

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Evaluate

t \times t^{2}

Use the product rule a^{n} \times a^{m} = a^{n + m} to simplify the expression

t^{1 + 2}

Add the numbers

t^{3}

- 2 t^{3}

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

Solution

- t^{2} + 2 t^{3}

Show Solution

Factor the expression

- t^{2} (1 - 2 t)

Evaluate

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

Subtract the terms

More Steps

Simplify

2 t - 3 t

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

(2 - 3) t

Subtract the numbers

- t

(t - 2 t^{2}) (- t)

Multiply the terms

- t (t - 2 t^{2})

Factor the expression

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Evaluate

t - 2 t^{2}

Rewrite the expression

t - t \times 2 t

Factor out t from the expression

t (1 - 2 t)

- t \times t (1 - 2 t)

Solution

- t^{2} (1 - 2 t)

Show Solution

Find the roots

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

Alternative Form

t_{1} = 0, t_{2} = 0.5

Evaluate

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

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

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

Subtract the terms

More Steps

Simplify

2 t - 3 t

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

(2 - 3) t

Subtract the numbers

- t

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

Multiply the terms

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

Change the sign

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

Separate the equation into 2 possible cases

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

Solve the equation

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Evaluate

t - 2 t^{2} = 0

Factor the expression

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Evaluate

t - 2 t^{2}

Rewrite the expression

t - t \times 2 t

Factor out t from the expression

t (1 - 2 t)

t (1 - 2 t) = 0

When the product of factors equals 0,at least one factor is 0

t = 0 1 - 2 t = 0

Solve the equation for t

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Evaluate

1 - 2 t = 0

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

- 2 t = 0 - 1

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

- 2 t = - 1

Change the signs on both sides of the equation

2 t = 1

Divide both sides

\frac{2 t}{2} = \frac{1}{2}

Divide the numbers

t = \frac{1}{2}

t = 0 t = \frac{1}{2}

t = 0 t = 0 t = \frac{1}{2}

Find the union

t = 0 t = \frac{1}{2}

Solution

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

Alternative Form

t_{1} = 0, t_{2} = 0.5

Show Solution