Solve 3x(2x-1)-(x+5)(2-x)-7x(x+1)=

$$3 x ( 2 x - 1 ) - ( x + 5 ) ( 2 - x ) - 7 x ( x + 1 ) =$$

Evaluate

$$-7x-10$$

Solution Steps

Use the distributive property to multiply 3x by 2x-1.

$$6x^{2}-3x-\left(x+5\right)\left(2-x\right)-7x\left(x+1\right)$$

Apply the distributive property by multiplying each term of x+5 by each term of 2-x.

$$6x^{2}-3x-\left(2x-x^{2}+10-5x\right)-7x\left(x+1\right)$$

Combine 2x and -5x to get -3x.

$$6x^{2}-3x-\left(-3x-x^{2}+10\right)-7x\left(x+1\right)$$

To find the opposite of -3x-x^{2}+10, find the opposite of each term.

$$6x^{2}-3x-\left(-3x\right)-\left(-x^{2}\right)-10-7x\left(x+1\right)$$

The opposite of -3x is 3x.

$$6x^{2}-3x+3x-\left(-x^{2}\right)-10-7x\left(x+1\right)$$

The opposite of -x^{2} is x^{2}.

$$6x^{2}-3x+3x+x^{2}-10-7x\left(x+1\right)$$

Combine -3x and 3x to get 0.

$$6x^{2}+x^{2}-10-7x\left(x+1\right)$$

Combine 6x^{2} and x^{2} to get 7x^{2}.

$$7x^{2}-10-7x\left(x+1\right)$$

Use the distributive property to multiply -7x by x+1.

$$7x^{2}-10-7x^{2}-7x$$

Combine 7x^{2} and -7x^{2} to get 0.

$$-10-7x$$

Expand

$$-7x-10$$

Solution Steps

Use the distributive property to multiply 3x by 2x-1.

$$6x^{2}-3x-\left(x+5\right)\left(2-x\right)-7x\left(x+1\right)$$

Apply the distributive property by multiplying each term of x+5 by each term of 2-x.

$$6x^{2}-3x-\left(2x-x^{2}+10-5x\right)-7x\left(x+1\right)$$

Combine 2x and -5x to get -3x.

$$6x^{2}-3x-\left(-3x-x^{2}+10\right)-7x\left(x+1\right)$$

To find the opposite of -3x-x^{2}+10, find the opposite of each term.

$$6x^{2}-3x-\left(-3x\right)-\left(-x^{2}\right)-10-7x\left(x+1\right)$$

The opposite of -3x is 3x.

$$6x^{2}-3x+3x-\left(-x^{2}\right)-10-7x\left(x+1\right)$$

The opposite of -x^{2} is x^{2}.

$$6x^{2}-3x+3x+x^{2}-10-7x\left(x+1\right)$$

Combine -3x and 3x to get 0.

$$6x^{2}+x^{2}-10-7x\left(x+1\right)$$

Combine 6x^{2} and x^{2} to get 7x^{2}.

$$7x^{2}-10-7x\left(x+1\right)$$

Use the distributive property to multiply -7x by x+1.

$$7x^{2}-10-7x^{2}-7x$$

Combine 7x^{2} and -7x^{2} to get 0.

$$-10-7x$$