Solve (6x^2-5x)2-7(6x^2-5x) 6

Question

Simplify the expression

- 240 x^{2} + 200 x

Evaluate

(6 x^{2} - 5 x) \times 2 - 7 (6 x^{2} - 5 x) \times 6

Multiply the terms

2 (6 x^{2} - 5 x) - 7 (6 x^{2} - 5 x) \times 6

Multiply the terms

2 (6 x^{2} - 5 x) - 42 (6 x^{2} - 5 x)

Expand the expression

More Steps

Calculate

2 (6 x^{2} - 5 x)

Apply the distributive property

2 \times 6 x^{2} - 2 \times 5 x

Multiply the numbers

12 x^{2} - 2 \times 5 x

Multiply the numbers

12 x^{2} - 10 x

12 x^{2} - 10 x - 42 (6 x^{2} - 5 x)

Expand the expression

More Steps

Calculate

- 42 (6 x^{2} - 5 x)

Apply the distributive property

- 42 \times 6 x^{2} - (- 42 \times 5 x)

Multiply the numbers

- 252 x^{2} - (- 42 \times 5 x)

Multiply the numbers

- 252 x^{2} - (- 210 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

- 252 x^{2} + 210 x

12 x^{2} - 10 x - 252 x^{2} + 210 x

Subtract the terms

More Steps

Evaluate

12 x^{2} - 252 x^{2}

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

(12 - 252) x^{2}

Subtract the numbers

- 240 x^{2}

- 240 x^{2} - 10 x + 210 x

Solution

More Steps

Evaluate

- 10 x + 210 x

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

(- 10 + 210) x

Add the numbers

200 x

- 240 x^{2} + 200 x

Show Solution

Factor the expression

- 40 x (6 x - 5)

Evaluate

(6 x^{2} - 5 x) \times 2 - 7 (6 x^{2} - 5 x) \times 6

Multiply the terms

2 (6 x^{2} - 5 x) - 7 (6 x^{2} - 5 x) \times 6

Multiply the terms

2 (6 x^{2} - 5 x) - 42 (6 x^{2} - 5 x)

Subtract the terms

- 20 (12 x^{2} - 10 x)

Factor the expression

More Steps

Evaluate

12 x^{2} - 10 x

Rewrite the expression

2 x \times 6 x - 2 x \times 5

Factor out 2 x from the expression

2 x (6 x - 5)

- 20 \times 2 x (6 x - 5)

Solution

- 40 x (6 x - 5)

Show Solution

Find the roots

x_{1} = 0, x_{2} = \frac{5}{6}

Alternative Form

x_{1} = 0, x_{2} = 0.8 \dot{3}

Evaluate

(6 x^{2} - 5 x) \times 2 - 7 (6 x^{2} - 5 x) \times 6

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

(6 x^{2} - 5 x) \times 2 - 7 (6 x^{2} - 5 x) \times 6 = 0

Multiply the terms

2 (6 x^{2} - 5 x) - 7 (6 x^{2} - 5 x) \times 6 = 0

Multiply the terms

2 (6 x^{2} - 5 x) - 42 (6 x^{2} - 5 x) = 0

Subtract the terms

- 20 (12 x^{2} - 10 x) = 0

Change the sign

20 (12 x^{2} - 10 x) = 0

Rewrite the expression

12 x^{2} - 10 x = 0

Factor the expression

More Steps

Evaluate

12 x^{2} - 10 x

Rewrite the expression

2 x \times 6 x - 2 x \times 5

Factor out 2 x from the expression

2 x (6 x - 5)

2 x (6 x - 5) = 0

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

2 x = 0 6 x - 5 = 0

Solve the equation for x

x = 0 6 x - 5 = 0

Solve the equation for x

More Steps

Evaluate

6 x - 5 = 0

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

6 x = 0 + 5

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

6 x = 5

Divide both sides

\frac{6 x}{6} = \frac{5}{6}

Divide the numbers

x = \frac{5}{6}

x = 0 x = \frac{5}{6}

Solution

x_{1} = 0, x_{2} = \frac{5}{6}

Alternative Form

x_{1} = 0, x_{2} = 0.8 \dot{3}

Show Solution