Solve 3q^22q7(5q-2)

Question

Simplify the expression

210 q^{4} - 84 q^{3}

Evaluate

3 q^{2} \times 2 q \times 7 (5 q - 2)

Multiply the terms

More Steps

Evaluate

3 \times 2 \times 7

Multiply the terms

6 \times 7

Multiply the numbers

42

42 q^{2} \times q (5 q - 2)

Multiply the terms with the same base by adding their exponents

42 q^{2 + 1} (5 q - 2)

Add the numbers

42 q^{3} (5 q - 2)

Apply the distributive property

42 q^{3} \times 5 q - 42 q^{3} \times 2

Multiply the terms

More Steps

Evaluate

42 q^{3} \times 5 q

Multiply the numbers

210 q^{3} \times q

Multiply the terms

More Steps

Evaluate

q^{3} \times q

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

q^{3 + 1}

Add the numbers

q^{4}

210 q^{4}

210 q^{4} - 42 q^{3} \times 2

Solution

210 q^{4} - 84 q^{3}

Show Solution

q_{1} = 0, q_{2} = \frac{2}{5}

Alternative Form

q_{1} = 0, q_{2} = 0.4

Evaluate

3 q^{2} \times 2 q \times 7 (5 q - 2)

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

3 q^{2} \times 2 q \times 7 (5 q - 2) = 0

Multiply

More Steps

Multiply the terms

3 q^{2} \times 2 q \times 7 (5 q - 2)

Multiply the terms

More Steps

Evaluate

3 \times 2 \times 7

Multiply the terms

6 \times 7

Multiply the numbers

42

42 q^{2} \times q (5 q - 2)

Multiply the terms with the same base by adding their exponents

42 q^{2 + 1} (5 q - 2)

Add the numbers

42 q^{3} (5 q - 2)

42 q^{3} (5 q - 2) = 0

Elimination the left coefficient

q^{3} (5 q - 2) = 0

Separate the equation into 2 possible cases

q^{3} = 0 5 q - 2 = 0

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

q = 0 5 q - 2 = 0

Solve the equation

More Steps

Evaluate

5 q - 2 = 0

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

5 q = 0 + 2

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

5 q = 2

Divide both sides

\frac{5 q}{5} = \frac{2}{5}

Divide the numbers

q = \frac{2}{5}

q = 0 q = \frac{2}{5}

Solution

q_{1} = 0, q_{2} = \frac{2}{5}

Alternative Form

q_{1} = 0, q_{2} = 0.4

Show Solution