Solve (23!*17!*19!*15!)=(506*323)*x*20!*14!*18!*16!

$$(23 ! \times 17 ! \times 19 ! \times 15 ! )=(506 \times 323) \times x \times 20 ! \times 14 ! \times 18 ! \times 16 !$$

Solve for x

$$x=315$$

Steps for Solving Linear Equation

The factorial of 23 is 25852016738884976640000.

$$25852016738884976640000\times 17!\times 19!\times 15!=506\times 323x\times 20!\times 14!\times 18!\times 16!$$

The factorial of 17 is 355687428096000.

$$25852016738884976640000\times 355687428096000\times 19!\times 15!=506\times 323x\times 20!\times 14!\times 18!\times 16!$$

Multiply 25852016738884976640000 and 355687428096000 to get 9195237344948738535854639677440000000.

$$9195237344948738535854639677440000000\times 19!\times 15!=506\times 323x\times 20!\times 14!\times 18!\times 16!$$

The factorial of 19 is 121645100408832000.

$$9195237344948738535854639677440000000\times 121645100408832000\times 15!=506\times 323x\times 20!\times 14!\times 18!\times 16!$$

Multiply 9195237344948738535854639677440000000 and 121645100408832000 to get 1118555570109331068277973902116680592607150080000000000.

$$1118555570109331068277973902116680592607150080000000000\times 15!=506\times 323x\times 20!\times 14!\times 18!\times 16!$$

The factorial of 15 is 1307674368000.

$$1118555570109331068277973902116680592607150080000000000\times 1307674368000=506\times 323x\times 20!\times 14!\times 18!\times 16!$$

Multiply 1118555570109331068277973902116680592607150080000000000 and 1307674368000 to get 1462706448215599195613164370770924156195420453145149440000000000000.

$$1462706448215599195613164370770924156195420453145149440000000000000=506\times 323x\times 20!\times 14!\times 18!\times 16!$$

Multiply 506 and 323 to get 163438.

$$1462706448215599195613164370770924156195420453145149440000000000000=163438x\times 20!\times 14!\times 18!\times 16!$$

The factorial of 20 is 2432902008176640000.

$$1462706448215599195613164370770924156195420453145149440000000000000=163438x\times 2432902008176640000\times 14!\times 18!\times 16!$$

Multiply 163438 and 2432902008176640000 to get 397628638412373688320000.

$$1462706448215599195613164370770924156195420453145149440000000000000=397628638412373688320000x\times 14!\times 18!\times 16!$$

The factorial of 14 is 87178291200.

$$1462706448215599195613164370770924156195420453145149440000000000000=397628638412373688320000x\times 87178291200\times 18!\times 16!$$

Multiply 397628638412373688320000 and 87178291200 to get 34664585228973419083578998784000000.

$$1462706448215599195613164370770924156195420453145149440000000000000=34664585228973419083578998784000000x\times 18!\times 16!$$

The factorial of 18 is 6402373705728000.

$$1462706448215599195613164370770924156195420453145149440000000000000=34664585228973419083578998784000000x\times 6402373705728000\times 16!$$

Multiply 34664585228973419083578998784000000 and 6402373705728000 to get 221935628989946640531344028197754085834752000000000.

$$1462706448215599195613164370770924156195420453145149440000000000000=221935628989946640531344028197754085834752000000000x\times 16!$$

The factorial of 16 is 20922789888000.

$$1462706448215599195613164370770924156195420453145149440000000000000=221935628989946640531344028197754085834752000000000x\times 20922789888000$$

Multiply 221935628989946640531344028197754085834752000000000 and 20922789888000 to get 4643512534017775224168775780225156051414033184587776000000000000.

$$1462706448215599195613164370770924156195420453145149440000000000000=4643512534017775224168775780225156051414033184587776000000000000x$$

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

$$4643512534017775224168775780225156051414033184587776000000000000x=1462706448215599195613164370770924156195420453145149440000000000000$$

Divide both sides by 4643512534017775224168775780225156051414033184587776000000000000.

$$x=\frac{1462706448215599195613164370770924156195420453145149440000000000000}{4643512534017775224168775780225156051414033184587776000000000000}$$

Divide 1462706448215599195613164370770924156195420453145149440000000000000 by 4643512534017775224168775780225156051414033184587776000000000000 to get 315.

$$x=315$$