Solve 30r^2 - 5r - 60

Question

Factor the expression

5 (2 r - 3) (3 r + 4)

Evaluate

30 r^{2} - 5 r - 60

Rewrite the expression

5 \times 6 r^{2} - 5 r - 5 \times 12

Factor out 5 from the expression

5 (6 r^{2} - r - 12)

Solution

More Steps

Evaluate

6 r^{2} - r - 12

Rewrite the expression

6 r^{2} + (8 - 9) r - 12

Calculate

6 r^{2} + 8 r - 9 r - 12

Rewrite the expression

2 r \times 3 r + 2 r \times 4 - 3 \times 3 r - 3 \times 4

Factor out 2 r from the expression

2 r (3 r + 4) - 3 \times 3 r - 3 \times 4

Factor out - 3 from the expression

2 r (3 r + 4) - 3 (3 r + 4)

Factor out 3 r + 4 from the expression

(2 r - 3) (3 r + 4)

5 (2 r - 3) (3 r + 4)

Show Solution

r_{1} = - \frac{4}{3}, r_{2} = \frac{3}{2}

Alternative Form

r_{1} = - 1. \dot{3}, r_{2} = 1.5

Evaluate

30 r^{2} - 5 r - 60

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

30 r^{2} - 5 r - 60 = 0

Factor the expression

More Steps

Evaluate

30 r^{2} - 5 r - 60

Rewrite the expression

5 \times 6 r^{2} - 5 r - 5 \times 12

Factor out 5 from the expression

5 (6 r^{2} - r - 12)

Factor the expression

More Steps

Evaluate

6 r^{2} - r - 12

Rewrite the expression

6 r^{2} + (8 - 9) r - 12

Calculate

6 r^{2} + 8 r - 9 r - 12

Rewrite the expression

2 r \times 3 r + 2 r \times 4 - 3 \times 3 r - 3 \times 4

Factor out 2 r from the expression

2 r (3 r + 4) - 3 \times 3 r - 3 \times 4

Factor out - 3 from the expression

2 r (3 r + 4) - 3 (3 r + 4)

Factor out 3 r + 4 from the expression

(2 r - 3) (3 r + 4)

5 (2 r - 3) (3 r + 4)

5 (2 r - 3) (3 r + 4) = 0

Divide the terms

(2 r - 3) (3 r + 4) = 0

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

2 r - 3 = 0 3 r + 4 = 0

Solve the equation for r

More Steps

Evaluate

2 r - 3 = 0

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

2 r = 0 + 3

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

2 r = 3

Divide both sides

\frac{2 r}{2} = \frac{3}{2}

Divide the numbers

r = \frac{3}{2}

r = \frac{3}{2} 3 r + 4 = 0

Solve the equation for r

More Steps

Evaluate

3 r + 4 = 0

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

3 r = 0 - 4

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

3 r = - 4

Divide both sides

\frac{3 r}{3} = \frac{- 4}{3}

Divide the numbers

r = \frac{- 4}{3}

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

r = - \frac{4}{3}

r = \frac{3}{2} r = - \frac{4}{3}

Solution

r_{1} = - \frac{4}{3}, r_{2} = \frac{3}{2}

Alternative Form

r_{1} = - 1. \dot{3}, r_{2} = 1.5

Show Solution