Solve -6(2x - 9 ) (7 - 6x)

Question

Simplify the expression

- 408 x + 72 x^{2} + 378

Evaluate

- 6 (2 x - 9) (7 - 6 x)

Multiply the terms

More Steps

Evaluate

- 6 (2 x - 9)

Apply the distributive property

- 6 \times 2 x - (- 6 \times 9)

Multiply the numbers

- 12 x - (- 6 \times 9)

Multiply the numbers

- 12 x - (- 54)

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

- 12 x + 54

(- 12 x + 54) (7 - 6 x)

Apply the distributive property

- 12 x \times 7 - (- 12 x \times 6 x) + 54 \times 7 - 54 \times 6 x

Multiply the numbers

- 84 x - (- 12 x \times 6 x) + 54 \times 7 - 54 \times 6 x

Multiply the terms

More Steps

Evaluate

- 12 x \times 6 x

Multiply the numbers

- 72 x \times x

Multiply the terms

- 72 x^{2}

- 84 x - (- 72 x^{2}) + 54 \times 7 - 54 \times 6 x

Multiply the numbers

- 84 x - (- 72 x^{2}) + 378 - 54 \times 6 x

Multiply the numbers

- 84 x - (- 72 x^{2}) + 378 - 324 x

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

- 84 x + 72 x^{2} + 378 - 324 x

Solution

More Steps

Evaluate

- 84 x - 324 x

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

(- 84 - 324) x

Subtract the numbers

- 408 x

- 408 x + 72 x^{2} + 378

Show Solution

Find the roots

x_{1} = \frac{7}{6}, x_{2} = \frac{9}{2}

Alternative Form

x_{1} = 1.1 \dot{6}, x_{2} = 4.5

Evaluate

- 6 (2 x - 9) (7 - 6 x)

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

- 6 (2 x - 9) (7 - 6 x) = 0

Change the sign

6 (2 x - 9) (7 - 6 x) = 0

Elimination the left coefficient

(2 x - 9) (7 - 6 x) = 0

Separate the equation into 2 possible cases

2 x - 9 = 0 7 - 6 x = 0

Solve the equation

More Steps

Evaluate

2 x - 9 = 0

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

2 x = 0 + 9

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

2 x = 9

Divide both sides

\frac{2 x}{2} = \frac{9}{2}

Divide the numbers

x = \frac{9}{2}

x = \frac{9}{2} 7 - 6 x = 0

Solve the equation

More Steps

Evaluate

7 - 6 x = 0

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

- 6 x = 0 - 7

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

- 6 x = - 7

Change the signs on both sides of the equation

6 x = 7

Divide both sides

\frac{6 x}{6} = \frac{7}{6}

Divide the numbers

x = \frac{7}{6}

x = \frac{9}{2} x = \frac{7}{6}

Solution

x_{1} = \frac{7}{6}, x_{2} = \frac{9}{2}

Alternative Form

x_{1} = 1.1 \dot{6}, x_{2} = 4.5

Show Solution