Solve {l}{{(2x+1)}{(2x+6)}-7{(x-2)}=4{(x+1)}{(x-1)}-9x}{y=pi}{text{Solvefor}ztext{where}}{z=y}

$$\left. \begin{array} { l } { {(2 x + 1)} {(2 x + 6)} - 7 {(x - 2)} = 4 {(x + 1)} {(x - 1)} - 9 x }\\ { y = \pi }\\ { \text{Solve for } z \text{ where} } \\ { z = y } \end{array} \right.$$

Solve for x, y, z

$$z=\pi \approx 3.141592654$$

Solution Steps

Consider the first equation. Use the distributive property to multiply 2x+1 by 2x+6 and combine like terms.

$$4x^{2}+14x+6-7\left(x-2\right)=4\left(x+1\right)\left(x-1\right)-9x$$

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

$$4x^{2}+14x+6-7x+14=4\left(x+1\right)\left(x-1\right)-9x$$

Combine 14x and -7x to get 7x.

$$4x^{2}+7x+6+14=4\left(x+1\right)\left(x-1\right)-9x$$

Add 6 and 14 to get 20.

$$4x^{2}+7x+20=4\left(x+1\right)\left(x-1\right)-9x$$

Use the distributive property to multiply 4 by x+1.

$$4x^{2}+7x+20=\left(4x+4\right)\left(x-1\right)-9x$$

Use the distributive property to multiply 4x+4 by x-1 and combine like terms.

$$4x^{2}+7x+20=4x^{2}-4-9x$$

Subtract 4x^{2} from both sides.

$$4x^{2}+7x+20-4x^{2}=-4-9x$$

Combine 4x^{2} and -4x^{2} to get 0.

$$7x+20=-4-9x$$

Add 9x to both sides.

$$7x+20+9x=-4$$

Combine 7x and 9x to get 16x.

$$16x+20=-4$$

Subtract 20 from both sides.

$$16x=-4-20$$

Subtract 20 from -4 to get -24.

$$16x=-24$$

Divide both sides by 16.

$$x=\frac{-24}{16}$$

Reduce the fraction \frac{-24}{16} to lowest terms by extracting and canceling out 8.

$$x=-\frac{3}{2}$$

The system is now solved.

$$x=-\frac{3}{2} y=\pi z=\pi$$