Solve (7t-6)(3t^2-t-6)

Question

Simplify the expression

21 t^{3} - 25 t^{2} - 36 t + 36

Evaluate

(7 t - 6) (3 t^{2} - t - 6)

Apply the distributive property

7 t \times 3 t^{2} - 7 t \times t - 7 t \times 6 - 6 \times 3 t^{2} - (- 6 t) - (- 6 \times 6)

Multiply the terms

More Steps

Evaluate

7 t \times 3 t^{2}

Multiply the numbers

21 t \times t^{2}

Multiply the terms

More Steps

Evaluate

t \times t^{2}

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

t^{1 + 2}

Add the numbers

t^{3}

21 t^{3}

21 t^{3} - 7 t \times t - 7 t \times 6 - 6 \times 3 t^{2} - (- 6 t) - (- 6 \times 6)

Multiply the terms

21 t^{3} - 7 t^{2} - 7 t \times 6 - 6 \times 3 t^{2} - (- 6 t) - (- 6 \times 6)

Multiply the numbers

21 t^{3} - 7 t^{2} - 42 t - 6 \times 3 t^{2} - (- 6 t) - (- 6 \times 6)

Multiply the numbers

21 t^{3} - 7 t^{2} - 42 t - 18 t^{2} - (- 6 t) - (- 6 \times 6)

Multiply the numbers

21 t^{3} - 7 t^{2} - 42 t - 18 t^{2} - (- 6 t) - (- 36)

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

21 t^{3} - 7 t^{2} - 42 t - 18 t^{2} + 6 t + 36

Subtract the terms

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Evaluate

- 7 t^{2} - 18 t^{2}

Collect like terms by calculating the sum or difference of their coefficients

(- 7 - 18) t^{2}

Subtract the numbers

- 25 t^{2}

21 t^{3} - 25 t^{2} - 42 t + 6 t + 36

Solution

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Evaluate

- 42 t + 6 t

Collect like terms by calculating the sum or difference of their coefficients

(- 42 + 6) t

Add the numbers

- 36 t

21 t^{3} - 25 t^{2} - 36 t + 36

Show Solution

Find the roots

t_{1} = \frac{1 - 73}{6}, t_{2} = \frac{6}{7}, t_{3} = \frac{1 + 73}{6}

Alternative Form

t_{1} \approx - 1.257334, t_{2} = 0. \dot{8} 5714 \dot{2}, t_{3} \approx 1.590667

Evaluate

(7 t - 6) (3 t^{2} - t - 6)

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

(7 t - 6) (3 t^{2} - t - 6) = 0

Separate the equation into 2 possible cases

7 t - 6 = 0 3 t^{2} - t - 6 = 0

Solve the equation

More Steps

Evaluate

7 t - 6 = 0

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

7 t = 0 + 6

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

7 t = 6

Divide both sides

\frac{7 t}{7} = \frac{6}{7}

Divide the numbers

t = \frac{6}{7}

t = \frac{6}{7} 3 t^{2} - t - 6 = 0

Solve the equation

More Steps

Evaluate

3 t^{2} - t - 6 = 0

Substitute a= 3,b= - 1 and c= - 6 into the quadratic formula t = \frac{- b \pm b ^{2} - 4 a c}{2 a}

t = \frac{1 \pm ( - 1 ) ^{2} - 4 \times 3 ( - 6 )}{2 \times 3}

Simplify the expression

t = \frac{1 \pm ( - 1 ) ^{2} - 4 \times 3 ( - 6 )}{6}

Simplify the expression

More Steps

Evaluate

(- 1)^{2} - 4 \times 3 (- 6)

Evaluate the power

1 - 4 \times 3 (- 6)

Multiply

1 - (- 72)

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

1 + 72

Add the numbers

73

t = \frac{1 \pm 73}{6}

Separate the equation into 2 possible cases

t = \frac{1 + 73}{6} t = \frac{1 - 73}{6}

t = \frac{6}{7} t = \frac{1 + 73}{6} t = \frac{1 - 73}{6}

Solution

t_{1} = \frac{1 - 73}{6}, t_{2} = \frac{6}{7}, t_{3} = \frac{1 + 73}{6}

Alternative Form

t_{1} \approx - 1.257334, t_{2} = 0. \dot{8} 5714 \dot{2}, t_{3} \approx 1.590667

Show Solution