Solve 3t^2 16t - 12

Question

Simplify the expression

48 t^{3} - 12

Evaluate

3 t^{2} \times 16 t - 12

Solution

More Steps

Evaluate

3 t^{2} \times 16 t

Multiply the terms

48 t^{2} \times t

Multiply the terms with the same base by adding their exponents

48 t^{2 + 1}

Add the numbers

48 t^{3}

48 t^{3} - 12

Show Solution

Factor the expression

12 (4 t^{3} - 1)

Evaluate

3 t^{2} \times 16 t - 12

Multiply

More Steps

Evaluate

3 t^{2} \times 16 t

Multiply the terms

48 t^{2} \times t

Multiply the terms with the same base by adding their exponents

48 t^{2 + 1}

Add the numbers

48 t^{3}

48 t^{3} - 12

Solution

12 (4 t^{3} - 1)

Show Solution

Find the roots

t = \frac{3 2}{2}

Alternative Form

t \approx 0.629961

Evaluate

3 t^{2} \times 16 t - 12

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

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

Multiply

More Steps

Multiply the terms

3 t^{2} \times 16 t

Multiply the terms

48 t^{2} \times t

Multiply the terms with the same base by adding their exponents

48 t^{2 + 1}

Add the numbers

48 t^{3}

48 t^{3} - 12 = 0

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

48 t^{3} = 0 + 12

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

48 t^{3} = 12

Divide both sides

\frac{48 t ^{3}}{48} = \frac{12}{48}

Divide the numbers

t^{3} = \frac{12}{48}

Cancel out the common factor 12

t^{3} = \frac{1}{4}

Take the 3 -th root on both sides of the equation

3 t^{3} = 3 \frac{1}{4}

Calculate

t = 3 \frac{1}{4}

Solution

More Steps

Evaluate

3 \frac{1}{4}

To take a root of a fraction,take the root of the numerator and denominator separately

\frac{3 1}{3 4}

Simplify the radical expression

\frac{1}{3 4}

Multiply by the Conjugate

\frac{3 4 ^{2}}{3 4 \times 3 4 ^{2}}

Simplify

\frac{2 3 2}{3 4 \times 3 4 ^{2}}

Multiply the numbers

More Steps

Evaluate

34 \times 3 4^{2}

The product of roots with the same index is equal to the root of the product

3 4 \times 4^{2}

Calculate the product

3 4^{3}

Transform the expression

3 2^{6}

Reduce the index of the radical and exponent with 3

2^{2}

\frac{2 3 2}{2 ^{2}}

Reduce the fraction

More Steps

Evaluate

\frac{2}{2 ^{2}}

Use the product rule \frac{a ^{n}}{a ^{m}} = a^{n - m} to simplify the expression

\frac{1}{2 ^{2 - 1}}

Subtract the terms

\frac{1}{2 ^{1}}

Simplify

\frac{1}{2}

\frac{3 2}{2}

t = \frac{3 2}{2}

Alternative Form

t \approx 0.629961

Show Solution