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

Question

Simplify the expression

8 t - 3 t^{2}

Evaluate

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

Remove the parentheses

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

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

7 t - 6 - 3 t^{2} + t + 6

Add the terms

More Steps

Evaluate

7 t + t

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

(7 + 1) t

Add the numbers

8 t

8 t - 6 - 3 t^{2} + 6

Solution

8 t - 3 t^{2}

Show Solution

Factor the expression

t (8 - 3 t)

Evaluate

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

Remove the parentheses

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

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

7 t - 6 - 3 t^{2} + t + 6

Add the terms

More Steps

Evaluate

7 t + t

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

(7 + 1) t

Add the numbers

8 t

8 t - 6 - 3 t^{2} + 6

Since two opposites add up to 0,remove them form the expression

8 t - 3 t^{2}

Rewrite the expression

t \times 8 - t \times 3 t

Solution

t (8 - 3 t)

Show Solution

Find the roots

t_{1} = 0, t_{2} = \frac{8}{3}

Alternative Form

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

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

Remove the parentheses

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

Subtract the terms

More Steps

Simplify

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

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

7 t - 6 - 3 t^{2} + t + 6

Add the terms

More Steps

Evaluate

7 t + t

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

(7 + 1) t

Add the numbers

8 t

8 t - 6 - 3 t^{2} + 6

Since two opposites add up to 0,remove them form the expression

8 t - 3 t^{2}

8 t - 3 t^{2} = 0

Factor the expression

More Steps

Evaluate

8 t - 3 t^{2}

Rewrite the expression

t \times 8 - t \times 3 t

Factor out t from the expression

t (8 - 3 t)

t (8 - 3 t) = 0

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

t = 0 8 - 3 t = 0

Solve the equation for t

More Steps

Evaluate

8 - 3 t = 0

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

- 3 t = 0 - 8

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

- 3 t = - 8

Change the signs on both sides of the equation

3 t = 8

Divide both sides

\frac{3 t}{3} = \frac{8}{3}

Divide the numbers

t = \frac{8}{3}

t = 0 t = \frac{8}{3}

Solution

t_{1} = 0, t_{2} = \frac{8}{3}

Alternative Form

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

Show Solution