Solve (3q^(2) 2q)/7 ⋅(5q-2)

Question

Simplify the expression

\frac{30 q ^{4} - 12 q ^{3}}{7}

Evaluate

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

Multiply

More Steps

Multiply the terms

3 q^{2} \times 2 q

Multiply the terms

6 q^{2} \times q

Multiply the terms with the same base by adding their exponents

6 q^{2 + 1}

Add the numbers

6 q^{3}

\frac{6 q ^{3}}{7} (5 q - 2)

Multiply the terms

\frac{6 q ^{3} ( 5 q - 2 )}{7}

Solution

More Steps

Evaluate

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

Apply the distributive property

6 q^{3} \times 5 q - 6 q^{3} \times 2

Multiply the terms

More Steps

Evaluate

6 q^{3} \times 5 q

Multiply the numbers

30 q^{3} \times q

Multiply the terms

30 q^{4}

30 q^{4} - 6 q^{3} \times 2

Multiply the numbers

30 q^{4} - 12 q^{3}

\frac{30 q ^{4} - 12 q ^{3}}{7}

Show Solution

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

Alternative Form

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

Evaluate

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

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

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

Multiply

More Steps

Multiply the terms

3 q^{2} \times 2 q

Multiply the terms

6 q^{2} \times q

Multiply the terms with the same base by adding their exponents

6 q^{2 + 1}

Add the numbers

6 q^{3}

\frac{6 q ^{3}}{7} (5 q - 2) = 0

Multiply the terms

\frac{6 q ^{3} ( 5 q - 2 )}{7} = 0

Simplify

6 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