Solve 5t^2 - 3t - 36

Question

Factor the expression

(t - 3) (5 t + 12)

Evaluate

5 t^{2} - 3 t - 36

Rewrite the expression

5 t^{2} + (12 - 15) t - 36

Calculate

5 t^{2} + 12 t - 15 t - 36

Rewrite the expression

t \times 5 t + t \times 12 - 3 \times 5 t - 3 \times 12

Factor out t from the expression

t (5 t + 12) - 3 \times 5 t - 3 \times 12

Factor out - 3 from the expression

t (5 t + 12) - 3 (5 t + 12)

Solution

(t - 3) (5 t + 12)

Show Solution

t_{1} = - \frac{12}{5}, t_{2} = 3

Alternative Form

t_{1} = - 2.4, t_{2} = 3

Evaluate

5 t^{2} - 3 t - 36

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

5 t^{2} - 3 t - 36 = 0

Factor the expression

More Steps

Evaluate

5 t^{2} - 3 t - 36

Rewrite the expression

5 t^{2} + (12 - 15) t - 36

Calculate

5 t^{2} + 12 t - 15 t - 36

Rewrite the expression

t \times 5 t + t \times 12 - 3 \times 5 t - 3 \times 12

Factor out t from the expression

t (5 t + 12) - 3 \times 5 t - 3 \times 12

Factor out - 3 from the expression

t (5 t + 12) - 3 (5 t + 12)

Factor out 5 t + 12 from the expression

(t - 3) (5 t + 12)

(t - 3) (5 t + 12) = 0

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

t - 3 = 0 5 t + 12 = 0

Solve the equation for t

More Steps

Evaluate

t - 3 = 0

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

t = 0 + 3

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

t = 3

t = 3 5 t + 12 = 0

Solve the equation for t

More Steps

Evaluate

5 t + 12 = 0

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

5 t = 0 - 12

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

5 t = - 12

Divide both sides

\frac{5 t}{5} = \frac{- 12}{5}

Divide the numbers

t = \frac{- 12}{5}

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

t = - \frac{12}{5}

t = 3 t = - \frac{12}{5}

Solution

t_{1} = - \frac{12}{5}, t_{2} = 3

Alternative Form

t_{1} = - 2.4, t_{2} = 3

Show Solution