Solve xleft(2x+3right)-2xleft(x-5right)-5left(2x+3right)+3left(x-5right)

$$x \left( 2x+3 \right) -2x \left( x-5 \right) -5 \left( 2x+3 \right) +3 \left( x-5 \right)$$

Evaluate

$$6\left(x-5\right)$$

Solution Steps

Use the distributive property to multiply x by 2x+3.

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

Use the distributive property to multiply -5 by 2x+3.

$$2x^{2}+3x-2x\left(x-5\right)-10x-15+3\left(x-5\right)$$

Use the distributive property to multiply 3 by x-5.

$$2x^{2}+3x-2x\left(x-5\right)-10x-15+3x-15$$

Combine -10x and 3x to get -7x.

$$2x^{2}+3x-2x\left(x-5\right)-7x-15-15$$

Subtract 15 from -15 to get -30.

$$2x^{2}+3x-2x\left(x-5\right)-7x-30$$

Use the distributive property to multiply -2x by x-5.

$$2x^{2}+3x-2x^{2}+10x-7x-30$$

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

$$3x+10x-7x-30$$

Combine 3x and 10x to get 13x.

$$13x-7x-30$$

Combine 13x and -7x to get 6x.

$$6x-30$$

Expand

$$6x-30$$

Solution Steps

Use the distributive property to multiply x by 2x+3.

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

Use the distributive property to multiply -5 by 2x+3.

$$2x^{2}+3x-2x\left(x-5\right)-10x-15+3\left(x-5\right)$$

Use the distributive property to multiply 3 by x-5.

$$2x^{2}+3x-2x\left(x-5\right)-10x-15+3x-15$$

Combine -10x and 3x to get -7x.

$$2x^{2}+3x-2x\left(x-5\right)-7x-15-15$$

Subtract 15 from -15 to get -30.

$$2x^{2}+3x-2x\left(x-5\right)-7x-30$$

Use the distributive property to multiply -2x by x-5.

$$2x^{2}+3x-2x^{2}+10x-7x-30$$

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

$$3x+10x-7x-30$$

Combine 3x and 10x to get 13x.

$$13x-7x-30$$

Combine 13x and -7x to get 6x.

$$6x-30$$