Solve (12x^2-7x-10)/3x^2

Question

Simplify the expression

\frac{12 x ^{4} - 7 x ^{3} - 10 x ^{2}}{3}

Evaluate

\frac{12 x ^{2} - 7 x - 10}{3} \times x^{2}

Multiply the terms

\frac{( 12 x ^{2} - 7 x - 10 ) x ^{2}}{3}

Multiply the terms

\frac{x ^{2} ( 12 x ^{2} - 7 x - 10 )}{3}

Solution

More Steps

Evaluate

x^{2} (12 x^{2} - 7 x - 10)

Apply the distributive property

x^{2} \times 12 x^{2} - x^{2} \times 7 x - x^{2} \times 10

Multiply the terms

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Evaluate

x^{2} \times 12 x^{2}

Use the commutative property to reorder the terms

12 x^{2} \times x^{2}

Multiply the terms

12 x^{4}

12 x^{4} - x^{2} \times 7 x - x^{2} \times 10

Multiply the terms

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Evaluate

x^{2} \times 7 x

Use the commutative property to reorder the terms

7 x^{2} \times x

Multiply the terms

7 x^{3}

12 x^{4} - 7 x^{3} - x^{2} \times 10

Use the commutative property to reorder the terms

12 x^{4} - 7 x^{3} - 10 x^{2}

\frac{12 x ^{4} - 7 x ^{3} - 10 x ^{2}}{3}

Show Solution

Find the roots

x_{1} = - \frac{2}{3}, x_{2} = 0, x_{3} = \frac{5}{4}

Alternative Form

x_{1} = - 0. \dot{6}, x_{2} = 0, x_{3} = 1.25

Evaluate

\frac{12 x ^{2} - 7 x - 10}{3} \times x^{2}

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

\frac{12 x ^{2} - 7 x - 10}{3} \times x^{2} = 0

Multiply the terms

More Steps

Multiply the terms

\frac{12 x ^{2} - 7 x - 10}{3} \times x^{2}

Multiply the terms

\frac{( 12 x ^{2} - 7 x - 10 ) x ^{2}}{3}

Multiply the terms

\frac{x ^{2} ( 12 x ^{2} - 7 x - 10 )}{3}

\frac{x ^{2} ( 12 x ^{2} - 7 x - 10 )}{3} = 0

Simplify

x^{2} (12 x^{2} - 7 x - 10) = 0

Separate the equation into 2 possible cases

x^{2} = 0 12 x^{2} - 7 x - 10 = 0

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

x = 0 12 x^{2} - 7 x - 10 = 0

Solve the equation

More Steps

Evaluate

12 x^{2} - 7 x - 10 = 0

Factor the expression

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Evaluate

12 x^{2} - 7 x - 10

Rewrite the expression

12 x^{2} + (- 15 + 8) x - 10

Calculate

12 x^{2} - 15 x + 8 x - 10

Rewrite the expression

3 x \times 4 x - 3 x \times 5 + 2 \times 4 x - 2 \times 5

Factor out 3 x from the expression

3 x (4 x - 5) + 2 \times 4 x - 2 \times 5

Factor out 2 from the expression

3 x (4 x - 5) + 2 (4 x - 5)

Factor out 4 x - 5 from the expression

(3 x + 2) (4 x - 5)

(3 x + 2) (4 x - 5) = 0

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

3 x + 2 = 0 4 x - 5 = 0

Solve the equation for x

More Steps

Evaluate

3 x + 2 = 0

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

3 x = 0 - 2

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

3 x = - 2

Divide both sides

\frac{3 x}{3} = \frac{- 2}{3}

Divide the numbers

x = \frac{- 2}{3}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

x = - \frac{2}{3}

x = - \frac{2}{3} 4 x - 5 = 0

Solve the equation for x

More Steps

Evaluate

4 x - 5 = 0

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

4 x = 0 + 5

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

4 x = 5

Divide both sides

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

Divide the numbers

x = \frac{5}{4}

x = - \frac{2}{3} x = \frac{5}{4}

x = 0 x = - \frac{2}{3} x = \frac{5}{4}

Solution

x_{1} = - \frac{2}{3}, x_{2} = 0, x_{3} = \frac{5}{4}

Alternative Form

x_{1} = - 0. \dot{6}, x_{2} = 0, x_{3} = 1.25

Show Solution