Solve 17(a-4) 6(6-2a)

Question

Simplify the expression

1428 a - 204 a^{2} - 2448

Evaluate

17 (a - 4) \times 6 (6 - 2 a)

Multiply the terms

102 (a - 4) (6 - 2 a)

Multiply the terms

More Steps

Evaluate

102 (a - 4)

Apply the distributive property

102 a - 102 \times 4

Multiply the numbers

102 a - 408

(102 a - 408) (6 - 2 a)

Apply the distributive property

102 a \times 6 - 102 a \times 2 a - 408 \times 6 - (- 408 \times 2 a)

Multiply the numbers

612 a - 102 a \times 2 a - 408 \times 6 - (- 408 \times 2 a)

Multiply the terms

More Steps

Evaluate

102 a \times 2 a

Multiply the numbers

204 a \times a

Multiply the terms

204 a^{2}

612 a - 204 a^{2} - 408 \times 6 - (- 408 \times 2 a)

Multiply the numbers

612 a - 204 a^{2} - 2448 - (- 408 \times 2 a)

Multiply the numbers

612 a - 204 a^{2} - 2448 - (- 816 a)

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

612 a - 204 a^{2} - 2448 + 816 a

Solution

More Steps

Evaluate

612 a + 816 a

Collect like terms by calculating the sum or difference of their coefficients

(612 + 816) a

Add the numbers

1428 a

1428 a - 204 a^{2} - 2448

Show Solution

Factor the expression

204 (a - 4) (3 - a)

Evaluate

17 (a - 4) \times 6 (6 - 2 a)

Multiply the terms

102 (a - 4) (6 - 2 a)

Factor the expression

102 (a - 4) \times 2 (3 - a)

Solution

204 (a - 4) (3 - a)

Show Solution

Find the roots

a_{1} = 3, a_{2} = 4

Evaluate

17 (a - 4) \times 6 (6 - 2 a)

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

17 (a - 4) \times 6 (6 - 2 a) = 0

Multiply the terms

102 (a - 4) (6 - 2 a) = 0

Elimination the left coefficient

(a - 4) (6 - 2 a) = 0

Separate the equation into 2 possible cases

a - 4 = 0 6 - 2 a = 0

Solve the equation

More Steps

Evaluate

a - 4 = 0

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

a = 0 + 4

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

a = 4

a = 4 6 - 2 a = 0

Solve the equation

More Steps

Evaluate

6 - 2 a = 0

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

- 2 a = 0 - 6

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

- 2 a = - 6

Change the signs on both sides of the equation

2 a = 6

Divide both sides

\frac{2 a}{2} = \frac{6}{2}

Divide the numbers

a = \frac{6}{2}

Divide the numbers

More Steps

Evaluate

\frac{6}{2}

Reduce the numbers

\frac{3}{1}

Calculate

3

a = 3

a = 4 a = 3

Solution

a_{1} = 3, a_{2} = 4

Show Solution