Solve 6a^2 - 6a = 36

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

a_{1} = - 2, a_{2} = 3

Evaluate

6 a^{2} - 6 a = 36

Move the expression to the left side

6 a^{2} - 6 a - 36 = 0

Factor the expression

More Steps

Evaluate

6 a^{2} - 6 a - 36

Rewrite the expression

6 a^{2} - 6 a - 6 \times 6

Factor out 6 from the expression

6 (a^{2} - a - 6)

Factor the expression

More Steps

Evaluate

a^{2} - a - 6

Rewrite the expression

a^{2} + (2 - 3) a - 6

Calculate

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

Rewrite the expression

a \times a + a \times 2 - 3 a - 3 \times 2

Factor out a from the expression

a (a + 2) - 3 a - 3 \times 2

Factor out - 3 from the expression

a (a + 2) - 3 (a + 2)

Factor out a + 2 from the expression

(a - 3) (a + 2)

6 (a - 3) (a + 2)

6 (a - 3) (a + 2) = 0

Divide the terms

(a - 3) (a + 2) = 0

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

a - 3 = 0 a + 2 = 0

Solve the equation for a

More Steps

Evaluate

a - 3 = 0

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

a = 0 + 3

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

a = 3

a = 3 a + 2 = 0

Solve the equation for a

More Steps

Evaluate

a + 2 = 0

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

a = 0 - 2

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

a = - 2

a = 3 a = - 2

Solution

a_{1} = - 2, a_{2} = 3

Show Solution