Solve p=(-3x-1)^2-3x(3x+7)

$$p = ( - 3 x - 1 ) ^ { 2 } - 3 x ( 3 x + 7 )$$

Solve for p

$$p=1-15x$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(-3x-1\right)^{2}.

$$p=9x^{2}+6x+1-3x\left(3x+7\right)$$

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

$$p=9x^{2}+6x+1-9x^{2}-21x$$

Combine 9x^{2} and -9x^{2} to get 0.

$$p=6x+1-21x$$

Combine 6x and -21x to get -15x.

$$p=-15x+1$$

Solve for x

$$x=\frac{1-p}{15}$$

Steps for Solving Linear Equation

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(-3x-1\right)^{2}.

$$p=9x^{2}+6x+1-3x\left(3x+7\right)$$

Swap sides so that all variable terms are on the left hand side.

$$9x^{2}+6x+1-3x\left(3x+7\right)=p$$

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

$$9x^{2}+6x+1-9x^{2}-21x=p$$

Combine 9x^{2} and -9x^{2} to get 0.

$$6x+1-21x=p$$

Combine 6x and -21x to get -15x.

$$-15x+1=p$$

Subtract 1 from both sides.

$$-15x=p-1$$

Divide both sides by -15.

$$\frac{-15x}{-15}=\frac{p-1}{-15}$$

Dividing by -15 undoes the multiplication by -15.

$$x=\frac{p-1}{-15}$$

Divide p-1 by -15.

$$x=\frac{1-p}{15}$$