Solve 6b^2 - 30 = -24b

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

b_{1} = - 5, b_{2} = 1

Evaluate

6 b^{2} - 30 = - 24 b

Move the expression to the left side

6 b^{2} - 30 + 24 b = 0

Factor the expression

More Steps

Evaluate

6 b^{2} - 30 + 24 b

Evaluate

6 b^{2} + 24 b - 30

Rewrite the expression

6 b^{2} + 6 \times 4 b - 6 \times 5

Factor out 6 from the expression

6 (b^{2} + 4 b - 5)

Factor the expression

More Steps

Evaluate

b^{2} + 4 b - 5

Rewrite the expression

b^{2} + (5 - 1) b - 5

Calculate

b^{2} + 5 b - b - 5

Rewrite the expression

b \times b + b \times 5 - b - 5

Factor out b from the expression

b (b + 5) - b - 5

Factor out - 1 from the expression

b (b + 5) - (b + 5)

Factor out b + 5 from the expression

(b - 1) (b + 5)

6 (b - 1) (b + 5)

6 (b - 1) (b + 5) = 0

Divide the terms

(b - 1) (b + 5) = 0

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

b - 1 = 0 b + 5 = 0

Solve the equation for b

More Steps

Evaluate

b - 1 = 0

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

b = 0 + 1

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

b = 1

b = 1 b + 5 = 0

Solve the equation for b

More Steps

Evaluate

b + 5 = 0

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

b = 0 - 5

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

b = - 5

b = 1 b = - 5

Solution

b_{1} = - 5, b_{2} = 1

Show Solution