Solve 11(16^{2}-16)+12(16^{3}-1)=x(16^5-16^2)+14(16^4-16)+15(16^3)

$$11 ( 16 ^ { 2 } - 16 ) + 12 ( 16 ^ { 3 } - 1 ) = x ( 16 ^ { 5 } - 16 ^ { 2 } ) + 14 ( 16 ^ { 4 } - 16 ) + 15 ( 16 ^ { 3 } )$$

Solve for x

$$x=-\frac{2207}{2496}\approx -0.884214744$$

Steps for Solving Linear Equation

Calculate 16 to the power of 2 and get 256.

$$11\left(256-16\right)+12\left(16^{3}-1\right)=x\left(16^{5}-16^{2}\right)+14\left(16^{4}-16\right)+15\times 16^{3}$$

Subtract 16 from 256 to get 240.

$$11\times 240+12\left(16^{3}-1\right)=x\left(16^{5}-16^{2}\right)+14\left(16^{4}-16\right)+15\times 16^{3}$$

Multiply 11 and 240 to get 2640.

$$2640+12\left(16^{3}-1\right)=x\left(16^{5}-16^{2}\right)+14\left(16^{4}-16\right)+15\times 16^{3}$$

Calculate 16 to the power of 3 and get 4096.

$$2640+12\left(4096-1\right)=x\left(16^{5}-16^{2}\right)+14\left(16^{4}-16\right)+15\times 16^{3}$$

Subtract 1 from 4096 to get 4095.

$$2640+12\times 4095=x\left(16^{5}-16^{2}\right)+14\left(16^{4}-16\right)+15\times 16^{3}$$

Multiply 12 and 4095 to get 49140.

$$2640+49140=x\left(16^{5}-16^{2}\right)+14\left(16^{4}-16\right)+15\times 16^{3}$$

Add 2640 and 49140 to get 51780.

$$51780=x\left(16^{5}-16^{2}\right)+14\left(16^{4}-16\right)+15\times 16^{3}$$

Calculate 16 to the power of 5 and get 1048576.

$$51780=x\left(1048576-16^{2}\right)+14\left(16^{4}-16\right)+15\times 16^{3}$$

Calculate 16 to the power of 2 and get 256.

$$51780=x\left(1048576-256\right)+14\left(16^{4}-16\right)+15\times 16^{3}$$

Subtract 256 from 1048576 to get 1048320.

$$51780=x\times 1048320+14\left(16^{4}-16\right)+15\times 16^{3}$$

Calculate 16 to the power of 4 and get 65536.

$$51780=x\times 1048320+14\left(65536-16\right)+15\times 16^{3}$$

Subtract 16 from 65536 to get 65520.

$$51780=x\times 1048320+14\times 65520+15\times 16^{3}$$

Multiply 14 and 65520 to get 917280.

$$51780=x\times 1048320+917280+15\times 16^{3}$$

Calculate 16 to the power of 3 and get 4096.

$$51780=x\times 1048320+917280+15\times 4096$$

Multiply 15 and 4096 to get 61440.

$$51780=x\times 1048320+917280+61440$$

Add 917280 and 61440 to get 978720.

$$51780=x\times 1048320+978720$$

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

$$x\times 1048320+978720=51780$$

Subtract 978720 from both sides.

$$x\times 1048320=51780-978720$$

Subtract 978720 from 51780 to get -926940.

$$x\times 1048320=-926940$$

Divide both sides by 1048320.

$$x=\frac{-926940}{1048320}$$

Reduce the fraction \frac{-926940}{1048320} to lowest terms by extracting and canceling out 420.

$$x=-\frac{2207}{2496}$$