Solve x(-21x-60)=-96

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

x_{1} = - 4, x_{2} = \frac{8}{7}

Alternative Form

x_{1} = - 4, x_{2} = 1. \dot{1} 4285 \dot{7}

Evaluate

x (- 21 x - 60) = - 96

Expand the expression

More Steps

Evaluate

x (- 21 x - 60)

Apply the distributive property

x (- 21 x) - x \times 60

Multiply the terms

More Steps

Evaluate

x (- 21 x)

Use the commutative property to reorder the terms

- 21 x \times x

Multiply the terms

- 21 x^{2}

- 21 x^{2} - x \times 60

Use the commutative property to reorder the terms

- 21 x^{2} - 60 x

- 21 x^{2} - 60 x = - 96

Move the expression to the left side

- 21 x^{2} - 60 x + 96 = 0

Factor the expression

More Steps

Evaluate

- 21 x^{2} - 60 x + 96

Rewrite the expression

- 3 \times 7 x^{2} - 3 \times 20 x + 3 \times 32

Factor out - 3 from the expression

- 3 (7 x^{2} + 20 x - 32)

Factor the expression

More Steps

Evaluate

7 x^{2} + 20 x - 32

Rewrite the expression

7 x^{2} + (- 8 + 28) x - 32

Calculate

7 x^{2} - 8 x + 28 x - 32

Rewrite the expression

x \times 7 x - x \times 8 + 4 \times 7 x - 4 \times 8

Factor out x from the expression

x (7 x - 8) + 4 \times 7 x - 4 \times 8

Factor out 4 from the expression

x (7 x - 8) + 4 (7 x - 8)

Factor out 7 x - 8 from the expression

(x + 4) (7 x - 8)

- 3 (x + 4) (7 x - 8)

- 3 (x + 4) (7 x - 8) = 0

Divide the terms

(x + 4) (7 x - 8) = 0

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

7 x - 8 = 0 x + 4 = 0

Solve the equation for x

More Steps

Evaluate

7 x - 8 = 0

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

7 x = 0 + 8

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

7 x = 8

Divide both sides

\frac{7 x}{7} = \frac{8}{7}

Divide the numbers

x = \frac{8}{7}

x = \frac{8}{7} x + 4 = 0

Solve the equation for x

More Steps

Evaluate

x + 4 = 0

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

x = 0 - 4

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

x = - 4

x = \frac{8}{7} x = - 4

Solution

x_{1} = - 4, x_{2} = \frac{8}{7}

Alternative Form

x_{1} = - 4, x_{2} = 1. \dot{1} 4285 \dot{7}

Show Solution