Solve 6a^2+9a-27 - ScanMath

Question

Factor the expression

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

Evaluate

6 a^{2} + 9 a - 27

Rewrite the expression

3 \times 2 a^{2} + 3 \times 3 a - 3 \times 9

Factor out 3 from the expression

3 (2 a^{2} + 3 a - 9)

Solution

More Steps

Evaluate

2 a^{2} + 3 a - 9

Rewrite the expression

2 a^{2} + (- 3 + 6) a - 9

Calculate

2 a^{2} - 3 a + 6 a - 9

Rewrite the expression

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

Factor out a from the expression

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

Factor out 3 from the expression

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

Factor out 2 a - 3 from the expression

(a + 3) (2 a - 3)

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

Show Solution

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

Alternative Form

a_{1} = - 3, a_{2} = 1.5

Evaluate

6 a^{2} + 9 a - 27

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

6 a^{2} + 9 a - 27 = 0

Factor the expression

More Steps

Evaluate

6 a^{2} + 9 a - 27

Rewrite the expression

3 \times 2 a^{2} + 3 \times 3 a - 3 \times 9

Factor out 3 from the expression

3 (2 a^{2} + 3 a - 9)

Factor the expression

More Steps

Evaluate

2 a^{2} + 3 a - 9

Rewrite the expression

2 a^{2} + (- 3 + 6) a - 9

Calculate

2 a^{2} - 3 a + 6 a - 9

Rewrite the expression

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

Factor out a from the expression

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

Factor out 3 from the expression

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

Factor out 2 a - 3 from the expression

(a + 3) (2 a - 3)

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

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

Divide the terms

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

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

a + 3 = 0 2 a - 3 = 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 2 a - 3 = 0

Solve the equation for a

More Steps

Evaluate

2 a - 3 = 0

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

2 a = 0 + 3

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

2 a = 3

Divide both sides

\frac{2 a}{2} = \frac{3}{2}

Divide the numbers

a = \frac{3}{2}

a = - 3 a = \frac{3}{2}

Solution

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

Alternative Form

a_{1} = - 3, a_{2} = 1.5

Show Solution