Solve {l}{x=-2}{y={(12*2(4-5x)^4+{(6x^2)}4^2(4-5x)^3{(5)})}}{text{Solvefor}ztext{where}}{z=y}

$$\left. \begin{array} { l } { x = -2 }\\ { y = {(12 \cdot 2 {(4 - 5 x)} ^ {4} + {(6 x ^ {2})} 4 ^ {2} {(4 - 5 x)} ^ {3} {(5)})} }\\ { \text{Solve for } z \text{ where} } \\ { z = y } \end{array} \right.$$

Solve for x, y, z

$$z=6190464$$

Solution Steps

Consider the second equation. Insert the known values of variables into the equation.

$$y=12\times 2\left(4-5\left(-2\right)\right)^{4}+6\left(-2\right)^{2}\times 4^{2}\left(4-5\left(-2\right)\right)^{3}\times 5$$

Multiply 12 and 2 to get 24.

$$y=24\left(4-5\left(-2\right)\right)^{4}+6\left(-2\right)^{2}\times 4^{2}\left(4-5\left(-2\right)\right)^{3}\times 5$$

Multiply -5 and -2 to get 10.

$$y=24\left(4+10\right)^{4}+6\left(-2\right)^{2}\times 4^{2}\left(4-5\left(-2\right)\right)^{3}\times 5$$

Add 4 and 10 to get 14.

$$y=24\times 14^{4}+6\left(-2\right)^{2}\times 4^{2}\left(4-5\left(-2\right)\right)^{3}\times 5$$

Calculate 14 to the power of 4 and get 38416.

$$y=24\times 38416+6\left(-2\right)^{2}\times 4^{2}\left(4-5\left(-2\right)\right)^{3}\times 5$$

Multiply 24 and 38416 to get 921984.

$$y=921984+6\left(-2\right)^{2}\times 4^{2}\left(4-5\left(-2\right)\right)^{3}\times 5$$

Calculate -2 to the power of 2 and get 4.

$$y=921984+6\times 4\times 4^{2}\left(4-5\left(-2\right)\right)^{3}\times 5$$

Multiply 6 and 4 to get 24.

$$y=921984+24\times 4^{2}\left(4-5\left(-2\right)\right)^{3}\times 5$$

Calculate 4 to the power of 2 and get 16.

$$y=921984+24\times 16\left(4-5\left(-2\right)\right)^{3}\times 5$$

Multiply 24 and 16 to get 384.

$$y=921984+384\left(4-5\left(-2\right)\right)^{3}\times 5$$

Multiply -5 and -2 to get 10.

$$y=921984+384\left(4+10\right)^{3}\times 5$$

Add 4 and 10 to get 14.

$$y=921984+384\times 14^{3}\times 5$$

Calculate 14 to the power of 3 and get 2744.

$$y=921984+384\times 2744\times 5$$

Multiply 384 and 2744 to get 1053696.

$$y=921984+1053696\times 5$$

Multiply 1053696 and 5 to get 5268480.

$$y=921984+5268480$$

Add 921984 and 5268480 to get 6190464.

$$y=6190464$$

Consider the third equation. Insert the known values of variables into the equation.

$$z=6190464$$

The system is now solved.

$$x=-2 y=6190464 z=6190464$$