Solve (5x+2)(-2x+3)+4(-2x+3)-7x(-2x+3

$$( 5 x + 2 ) ( - 2 x + 3 ) + 4 ( - 2 x + 3 ) - 7 x ( - 2 x + 3$$

Evaluate

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

Solution Steps

Apply the distributive property by multiplying each term of 5x+2 by each term of -2x+3.

$$-10x^{2}+15x-4x+6+4\left(-2x+3\right)-7x\left(-2x+3\right)$$

Combine 15x and -4x to get 11x.

$$-10x^{2}+11x+6+4\left(-2x+3\right)-7x\left(-2x+3\right)$$

Use the distributive property to multiply 4 by -2x+3.

$$-10x^{2}+11x+6-8x+12-7x\left(-2x+3\right)$$

Combine 11x and -8x to get 3x.

$$-10x^{2}+3x+6+12-7x\left(-2x+3\right)$$

Add 6 and 12 to get 18.

$$-10x^{2}+3x+18-7x\left(-2x+3\right)$$

Use the distributive property to multiply -7x by -2x+3.

$$-10x^{2}+3x+18+14x^{2}-21x$$

Combine -10x^{2} and 14x^{2} to get 4x^{2}.

$$4x^{2}+3x+18-21x$$

Combine 3x and -21x to get -18x.

$$4x^{2}-18x+18$$

Expand

$$4x^{2}-18x+18$$

Solution Steps

Apply the distributive property by multiplying each term of 5x+2 by each term of -2x+3.

$$-10x^{2}+15x-4x+6+4\left(-2x+3\right)-7x\left(-2x+3\right)$$

Combine 15x and -4x to get 11x.

$$-10x^{2}+11x+6+4\left(-2x+3\right)-7x\left(-2x+3\right)$$

Use the distributive property to multiply 4 by -2x+3.

$$-10x^{2}+11x+6-8x+12-7x\left(-2x+3\right)$$

Combine 11x and -8x to get 3x.

$$-10x^{2}+3x+6+12-7x\left(-2x+3\right)$$

Add 6 and 12 to get 18.

$$-10x^{2}+3x+18-7x\left(-2x+3\right)$$

Use the distributive property to multiply -7x by -2x+3.

$$-10x^{2}+3x+18+14x^{2}-21x$$

Combine -10x^{2} and 14x^{2} to get 4x^{2}.

$$4x^{2}+3x+18-21x$$

Combine 3x and -21x to get -18x.

$$4x^{2}-18x+18$$