Solve 3m^210m^3=2m

Question

Solve the equation

m_{1} = - \frac{4 3375}{15}, m_{2} = 0, m_{3} = \frac{4 3375}{15}

Alternative Form

m_{1} \approx - 0.508133, m_{2} = 0, m_{3} \approx 0.508133

Evaluate

3 m^{2} \times 10 m^{3} = 2 m

Multiply

More Steps

Evaluate

3 m^{2} \times 10 m^{3}

Multiply the terms

30 m^{2} \times m^{3}

Multiply the terms with the same base by adding their exponents

30 m^{2 + 3}

Add the numbers

30 m^{5}

30 m^{5} = 2 m

Add or subtract both sides

30 m^{5} - 2 m = 0

Factor the expression

2 m (15 m^{4} - 1) = 0

Divide both sides

m (15 m^{4} - 1) = 0

Separate the equation into 2 possible cases

m = 0 15 m^{4} - 1 = 0

Solve the equation

More Steps

Evaluate

15 m^{4} - 1 = 0

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

15 m^{4} = 0 + 1

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

15 m^{4} = 1

Divide both sides

\frac{15 m ^{4}}{15} = \frac{1}{15}

Divide the numbers

m^{4} = \frac{1}{15}

Take the root of both sides of the equation and remember to use both positive and negative roots

m = \pm 4 \frac{1}{15}

Simplify the expression

More Steps

Evaluate

4 \frac{1}{15}

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

\frac{4 1}{4 15}

Simplify the radical expression

\frac{1}{4 15}

Multiply by the Conjugate

\frac{4 1 5 ^{3}}{4 15 \times 4 1 5 ^{3}}

Simplify

\frac{4 3375}{4 15 \times 4 1 5 ^{3}}

Multiply the numbers

\frac{4 3375}{15}

m = \pm \frac{4 3375}{15}

Separate the equation into 2 possible cases

m = \frac{4 3375}{15} m = - \frac{4 3375}{15}

m = 0 m = \frac{4 3375}{15} m = - \frac{4 3375}{15}

Solution

m_{1} = - \frac{4 3375}{15}, m_{2} = 0, m_{3} = \frac{4 3375}{15}

Alternative Form

m_{1} \approx - 0.508133, m_{2} = 0, m_{3} \approx 0.508133

Show Solution