Solve 3t^2-5t-2 - ScanMath

Question

Factor the expression

(t - 2) (3 t + 1)

Evaluate

3 t^{2} - 5 t - 2

Rewrite the expression

3 t^{2} + (1 - 6) t - 2

Calculate

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

Rewrite the expression

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

Factor out t from the expression

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

Factor out - 2 from the expression

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

Solution

(t - 2) (3 t + 1)

Show Solution

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

Alternative Form

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

Evaluate

3 t^{2} - 5 t - 2

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

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

Factor the expression

More Steps

Evaluate

3 t^{2} - 5 t - 2

Rewrite the expression

3 t^{2} + (1 - 6) t - 2

Calculate

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

Rewrite the expression

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

Factor out t from the expression

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

Factor out - 2 from the expression

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

Factor out 3 t + 1 from the expression

(t - 2) (3 t + 1)

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

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

t - 2 = 0 3 t + 1 = 0

Solve the equation for t

More Steps

Evaluate

t - 2 = 0

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

t = 0 + 2

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

t = 2

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

Solution

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

Alternative Form

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

Show Solution