Solve ((144:((4*x+12)*2)+18):4-3)*56=112

$$( ( 144 : ( ( 4 \cdot x + 12 ) \cdot 2 ) + 18 ) : 4 - 3 ) \cdot 56 = 112$$

Solve for x

$$x=6$$

Steps for Solving Linear Equation

Divide both sides by 56.

$$\frac{\frac{144}{\left(4x+12\right)\times 2}+18}{4}-3=\frac{112}{56}$$

Divide 112 by 56 to get 2.

$$\frac{\frac{144}{\left(4x+12\right)\times 2}+18}{4}-3=2$$

Multiply both sides of the equation by 4.

$$\frac{144}{\left(4x+12\right)\times 2}+18-12=8$$

Use the distributive property to multiply 4x+12 by 2.

$$\frac{144}{8x+24}+18-12=8$$

Factor 8x+24.

$$\frac{144}{8\left(x+3\right)}+18-12=8$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 18 times \frac{8\left(x+3\right)}{8\left(x+3\right)}.

$$\frac{144}{8\left(x+3\right)}+\frac{18\times 8\left(x+3\right)}{8\left(x+3\right)}-12=8$$

Since \frac{144}{8\left(x+3\right)} and \frac{18\times 8\left(x+3\right)}{8\left(x+3\right)} have the same denominator, add them by adding their numerators.

$$\frac{144+18\times 8\left(x+3\right)}{8\left(x+3\right)}-12=8$$

Do the multiplications in 144+18\times 8\left(x+3\right).

$$\frac{144+144x+432}{8\left(x+3\right)}-12=8$$

Combine like terms in 144+144x+432.

$$\frac{576+144x}{8\left(x+3\right)}-12=8$$

Factor the expressions that are not already factored in \frac{576+144x}{8\left(x+3\right)}.

$$\frac{144\left(x+4\right)}{8\left(x+3\right)}-12=8$$

Cancel out 8 in both numerator and denominator.

$$\frac{18\left(x+4\right)}{x+3}-12=8$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 12 times \frac{x+3}{x+3}.

$$\frac{18\left(x+4\right)}{x+3}-\frac{12\left(x+3\right)}{x+3}=8$$

Since \frac{18\left(x+4\right)}{x+3} and \frac{12\left(x+3\right)}{x+3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{18\left(x+4\right)-12\left(x+3\right)}{x+3}=8$$

Do the multiplications in 18\left(x+4\right)-12\left(x+3\right).

$$\frac{18x+72-12x-36}{x+3}=8$$

Combine like terms in 18x+72-12x-36.

$$\frac{6x+36}{x+3}=8$$

Variable x cannot be equal to -3 since division by zero is not defined. Multiply both sides of the equation by x+3.

$$6x+36=8\left(x+3\right)$$

Use the distributive property to multiply 8 by x+3.

$$6x+36=8x+24$$

Subtract 8x from both sides.

$$6x+36-8x=24$$

Combine 6x and -8x to get -2x.

$$-2x+36=24$$

Subtract 36 from both sides.

$$-2x=24-36$$

Subtract 36 from 24 to get -12.

$$-2x=-12$$

Divide both sides by -2.

$$x=\frac{-12}{-2}$$

Divide -12 by -2 to get 6.

$$x=6$$