Solve 6t^2-13t-5 - ScanMath

Question

Factor the expression

(2 t - 5) (3 t + 1)

Evaluate

6 t^{2} - 13 t - 5

Rewrite the expression

6 t^{2} + (2 - 15) t - 5

Calculate

6 t^{2} + 2 t - 15 t - 5

Rewrite the expression

2 t \times 3 t + 2 t - 5 \times 3 t - 5

Factor out 2 t from the expression

2 t (3 t + 1) - 5 \times 3 t - 5

Factor out - 5 from the expression

2 t (3 t + 1) - 5 (3 t + 1)

Solution

(2 t - 5) (3 t + 1)

Show Solution

t_{1} = - \frac{1}{3}, t_{2} = \frac{5}{2}

Alternative Form

t_{1} = - 0. \dot{3}, t_{2} = 2.5

Evaluate

6 t^{2} - 13 t - 5

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

6 t^{2} - 13 t - 5 = 0

Factor the expression

More Steps

Evaluate

6 t^{2} - 13 t - 5

Rewrite the expression

6 t^{2} + (2 - 15) t - 5

Calculate

6 t^{2} + 2 t - 15 t - 5

Rewrite the expression

2 t \times 3 t + 2 t - 5 \times 3 t - 5

Factor out 2 t from the expression

2 t (3 t + 1) - 5 \times 3 t - 5

Factor out - 5 from the expression

2 t (3 t + 1) - 5 (3 t + 1)

Factor out 3 t + 1 from the expression

(2 t - 5) (3 t + 1)

(2 t - 5) (3 t + 1) = 0

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

2 t - 5 = 0 3 t + 1 = 0

Solve the equation for t

More Steps

Evaluate

2 t - 5 = 0

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

2 t = 0 + 5

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

2 t = 5

Divide both sides

\frac{2 t}{2} = \frac{5}{2}

Divide the numbers

t = \frac{5}{2}

t = \frac{5}{2} 3 t + 1 = 0

Solve the equation for t

More Steps

Evaluate

3 t + 1 = 0

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

3 t = 0 - 1

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

3 t = - 1

Divide both sides

\frac{3 t}{3} = \frac{- 1}{3}

Divide the numbers

t = \frac{- 1}{3}

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

t = - \frac{1}{3}

t = \frac{5}{2} t = - \frac{1}{3}

Solution

t_{1} = - \frac{1}{3}, t_{2} = \frac{5}{2}

Alternative Form

t_{1} = - 0. \dot{3}, t_{2} = 2.5

Show Solution