Solve g5 14/12g-g

Question

Simplify the expression

\frac{37}{6} g^{2} - g

Evaluate

g \times 5 \frac{14}{12} \times g - g

Covert the mixed number to an improper fraction

More Steps

Convert the expressions

5 \frac{14}{12}

Multiply the denominator of the fraction by the whole number and add the numerator of the fraction

\frac{5 \times 12 + 14}{12}

Multiply the terms

\frac{60 + 14}{12}

Add the terms

\frac{74}{12}

g \times \frac{74}{12} g - g

Solution

More Steps

Multiply the terms

g \times \frac{74}{12} g

Multiply the terms

g^{2} \times \frac{74}{12}

Use the commutative property to reorder the terms

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Evaluate

1 \times \frac{74}{12}

Any expression multiplied by 1 remains the same

\frac{74}{12}

Reduce the fraction

\frac{37}{6}

\frac{37}{6} g^{2}

\frac{37}{6} g^{2} - g

Show Solution

Factor the expression

\frac{1}{6} g (37 g - 6)

Evaluate

g \times 5 \frac{14}{12} \times g - g

Covert the mixed number to an improper fraction

More Steps

Convert the expressions

5 \frac{14}{12}

Multiply the denominator of the fraction by the whole number and add the numerator of the fraction

\frac{5 \times 12 + 14}{12}

Multiply the terms

\frac{60 + 14}{12}

Add the terms

\frac{74}{12}

g \times \frac{74}{12} g - g

Multiply

More Steps

Multiply the terms

g \times \frac{74}{12} g

Multiply the terms

g^{2} \times \frac{74}{12}

Use the commutative property to reorder the terms

More Steps

Evaluate

1 \times \frac{74}{12}

Any expression multiplied by 1 remains the same

\frac{74}{12}

Reduce the fraction

\frac{37}{6}

\frac{37}{6} g^{2}

\frac{37}{6} g^{2} - g

Rewrite the expression

\frac{1}{6} g \times 37 g - \frac{1}{6} g \times 6

Solution

\frac{1}{6} g (37 g - 6)

Show Solution

Find the roots

g_{1} = 0, g_{2} = \frac{6}{37}

Alternative Form

g_{1} = 0, g_{2} = 0. \dot{1} 6 \dot{2}

Evaluate

g \times 5 \frac{14}{12} \times g - g

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

g \times 5 \frac{14}{12} \times g - g = 0

Covert the mixed number to an improper fraction

More Steps

Convert the expressions

5 \frac{14}{12}

Multiply the denominator of the fraction by the whole number and add the numerator of the fraction

\frac{5 \times 12 + 14}{12}

Multiply the terms

\frac{60 + 14}{12}

Add the terms

\frac{74}{12}

g \times \frac{74}{12} g - g = 0

Multiply

More Steps

Multiply the terms

g \times \frac{74}{12} g

Multiply the terms

g^{2} \times \frac{74}{12}

Use the commutative property to reorder the terms

More Steps

Evaluate

1 \times \frac{74}{12}

Any expression multiplied by 1 remains the same

\frac{74}{12}

Reduce the fraction

\frac{37}{6}

\frac{37}{6} g^{2}

\frac{37}{6} g^{2} - g = 0

Factor the expression

More Steps

Evaluate

\frac{37}{6} g^{2} - g

Rewrite the expression

\frac{1}{6} g \times 37 g - \frac{1}{6} g \times 6

Factor out \frac{1}{6} g from the expression

\frac{1}{6} g (37 g - 6)

\frac{1}{6} g (37 g - 6) = 0

When the product of factors equals 0,at least one factor is 0

\frac{1}{6} g = 0 37 g - 6 = 0

Solve the equation for g

g = 0 37 g - 6 = 0

Solve the equation for g

More Steps

Evaluate

37 g - 6 = 0

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

37 g = 0 + 6

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

37 g = 6

Divide both sides

\frac{37 g}{37} = \frac{6}{37}

Divide the numbers

g = \frac{6}{37}

g = 0 g = \frac{6}{37}

Solution

g_{1} = 0, g_{2} = \frac{6}{37}

Alternative Form

g_{1} = 0, g_{2} = 0. \dot{1} 6 \dot{2}

Show Solution