Solve 3x^(2) 5x-12

Question

Simplify the expression

15 x^{3} - 12

Evaluate

3 x^{2} \times 5 x - 12

Solution

More Steps

Evaluate

3 x^{2} \times 5 x

Multiply the terms

15 x^{2} \times x

Multiply the terms with the same base by adding their exponents

15 x^{2 + 1}

Add the numbers

15 x^{3}

15 x^{3} - 12

Show Solution

Factor the expression

3 (5 x^{3} - 4)

Evaluate

3 x^{2} \times 5 x - 12

Multiply

More Steps

Evaluate

3 x^{2} \times 5 x

Multiply the terms

15 x^{2} \times x

Multiply the terms with the same base by adding their exponents

15 x^{2 + 1}

Add the numbers

15 x^{3}

15 x^{3} - 12

Solution

3 (5 x^{3} - 4)

Show Solution

Find the roots

x = \frac{3 100}{5}

Alternative Form

x \approx 0.928318

Evaluate

3 x^{2} \times 5 x - 12

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

3 x^{2} \times 5 x - 12 = 0

Multiply

More Steps

Multiply the terms

3 x^{2} \times 5 x

Multiply the terms

15 x^{2} \times x

Multiply the terms with the same base by adding their exponents

15 x^{2 + 1}

Add the numbers

15 x^{3}

15 x^{3} - 12 = 0

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

15 x^{3} = 0 + 12

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

15 x^{3} = 12

Divide both sides

\frac{15 x ^{3}}{15} = \frac{12}{15}

Divide the numbers

x^{3} = \frac{12}{15}

Cancel out the common factor 3

x^{3} = \frac{4}{5}

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

3 x^{3} = 3 \frac{4}{5}

Calculate

x = 3 \frac{4}{5}

Solution

More Steps

Evaluate

3 \frac{4}{5}

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

\frac{3 4}{3 5}

Multiply by the Conjugate

\frac{3 4 \times 3 5 ^{2}}{3 5 \times 3 5 ^{2}}

Simplify

\frac{3 4 \times 3 25}{3 5 \times 3 5 ^{2}}

Multiply the numbers

More Steps

Evaluate

34 \times 325

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

3 4 \times 25

Calculate the product

3100

\frac{3 100}{3 5 \times 3 5 ^{2}}

Multiply the numbers

More Steps

Evaluate

35 \times 3 5^{2}

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

3 5 \times 5^{2}

Calculate the product

3 5^{3}

Reduce the index of the radical and exponent with 3

5

\frac{3 100}{5}

x = \frac{3 100}{5}

Alternative Form

x \approx 0.928318

Show Solution