Solve -(7-x) (3x-14)

Question

Simplify the expression

- 35 x + 98 + 3 x^{2}

Evaluate

- (7 - x) (3 x - 14)

Calculate

(- 7 + x) (3 x - 14)

Apply the distributive property

- 7 \times 3 x - (- 7 \times 14) + x \times 3 x - x \times 14

Multiply the numbers

- 21 x - (- 7 \times 14) + x \times 3 x - x \times 14

Multiply the numbers

- 21 x - (- 98) + x \times 3 x - x \times 14

Multiply the terms

More Steps

Evaluate

x \times 3 x

Use the commutative property to reorder the terms

3 x \times x

Multiply the terms

3 x^{2}

- 21 x - (- 98) + 3 x^{2} - x \times 14

Use the commutative property to reorder the terms

- 21 x - (- 98) + 3 x^{2} - 14 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

- 21 x + 98 + 3 x^{2} - 14 x

Solution

More Steps

Evaluate

- 21 x - 14 x

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

(- 21 - 14) x

Subtract the numbers

- 35 x

- 35 x + 98 + 3 x^{2}

Show Solution

Find the roots

x_{1} = \frac{14}{3}, x_{2} = 7

Alternative Form

x_{1} = 4. \dot{6}, x_{2} = 7

Evaluate

- (7 - x) (3 x - 14)

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

- (7 - x) (3 x - 14) = 0

Calculate

(- 7 + x) (3 x - 14) = 0

Change the sign

(7 - x) (3 x - 14) = 0

Separate the equation into 2 possible cases

7 - x = 0 3 x - 14 = 0

Solve the equation

More Steps

Evaluate

7 - x = 0

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

- x = 0 - 7

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

- x = - 7

Change the signs on both sides of the equation

x = 7

x = 7 3 x - 14 = 0

Solve the equation

More Steps

Evaluate

3 x - 14 = 0

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

3 x = 0 + 14

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

3 x = 14

Divide both sides

\frac{3 x}{3} = \frac{14}{3}

Divide the numbers

x = \frac{14}{3}

x = 7 x = \frac{14}{3}

Solution

x_{1} = \frac{14}{3}, x_{2} = 7

Alternative Form

x_{1} = 4. \dot{6}, x_{2} = 7

Show Solution