Solve 0.6*40(1-4/300w)+0.4[90(1+1/3)-60(1+2/300x)]*(1+12/500x)=24+24

$$0.6 \times 40 ( 1 - \frac { 4 } { 300 } w ) + 0.4 [ 90 ( 1 + \frac { 1 } { 3 } ) - 60 ( 1 + \frac { 2 } { 300 } x ) ] \cdot ( 1 + \frac { 12 } { 500 } x ) = 24 + 24$$

Solve for w

$$w=\frac{x\left(325-3x\right)}{250}$$

Steps for Solving Linear Equation

Multiply 0.6 and 40 to get 24.

$$24\left(1-\frac{4}{300}w\right)+0.4\left(90\left(1+\frac{1}{3}\right)-60\left(1+\frac{2}{300}x\right)\right)\left(1+\frac{12}{500}x\right)=24+24$$

Reduce the fraction \frac{4}{300} to lowest terms by extracting and canceling out 4.

$$24\left(1-\frac{1}{75}w\right)+0.4\left(90\left(1+\frac{1}{3}\right)-60\left(1+\frac{2}{300}x\right)\right)\left(1+\frac{12}{500}x\right)=24+24$$

Use the distributive property to multiply 24 by 1-\frac{1}{75}w.

$$24-\frac{8}{25}w+0.4\left(90\left(1+\frac{1}{3}\right)-60\left(1+\frac{2}{300}x\right)\right)\left(1+\frac{12}{500}x\right)=24+24$$

Add 1 and \frac{1}{3} to get \frac{4}{3}.

$$24-\frac{8}{25}w+0.4\left(90\times \frac{4}{3}-60\left(1+\frac{2}{300}x\right)\right)\left(1+\frac{12}{500}x\right)=24+24$$

Multiply 90 and \frac{4}{3} to get 120.

$$24-\frac{8}{25}w+0.4\left(120-60\left(1+\frac{2}{300}x\right)\right)\left(1+\frac{12}{500}x\right)=24+24$$

Reduce the fraction \frac{2}{300} to lowest terms by extracting and canceling out 2.

$$24-\frac{8}{25}w+0.4\left(120-60\left(1+\frac{1}{150}x\right)\right)\left(1+\frac{12}{500}x\right)=24+24$$

Use the distributive property to multiply -60 by 1+\frac{1}{150}x.

$$24-\frac{8}{25}w+0.4\left(120-60-\frac{2}{5}x\right)\left(1+\frac{12}{500}x\right)=24+24$$

Subtract 60 from 120 to get 60.

$$24-\frac{8}{25}w+0.4\left(60-\frac{2}{5}x\right)\left(1+\frac{12}{500}x\right)=24+24$$

Reduce the fraction \frac{12}{500} to lowest terms by extracting and canceling out 4.

$$24-\frac{8}{25}w+0.4\left(60-\frac{2}{5}x\right)\left(1+\frac{3}{125}x\right)=24+24$$

Use the distributive property to multiply 0.4 by 60-\frac{2}{5}x.

$$24-\frac{8}{25}w+\left(24-\frac{4}{25}x\right)\left(1+\frac{3}{125}x\right)=24+24$$

Use the distributive property to multiply 24-\frac{4}{25}x by 1+\frac{3}{125}x and combine like terms.

$$24-\frac{8}{25}w+24+\frac{52}{125}x-\frac{12}{3125}x^{2}=24+24$$

Add 24 and 24 to get 48.

$$48-\frac{8}{25}w+\frac{52}{125}x-\frac{12}{3125}x^{2}=24+24$$

Add 24 and 24 to get 48.

$$48-\frac{8}{25}w+\frac{52}{125}x-\frac{12}{3125}x^{2}=48$$

Subtract 48 from both sides.

$$-\frac{8}{25}w+\frac{52}{125}x-\frac{12}{3125}x^{2}=48-48$$

Subtract 48 from 48 to get 0.

$$-\frac{8}{25}w+\frac{52}{125}x-\frac{12}{3125}x^{2}=0$$

Subtract \frac{52}{125}x from both sides. Anything subtracted from zero gives its negation.

$$-\frac{8}{25}w-\frac{12}{3125}x^{2}=-\frac{52}{125}x$$

Add \frac{12}{3125}x^{2} to both sides.

$$-\frac{8}{25}w=-\frac{52}{125}x+\frac{12}{3125}x^{2}$$

The equation is in standard form.

$$-\frac{8}{25}w=\frac{12x^{2}}{3125}-\frac{52x}{125}$$

Divide both sides of the equation by -\frac{8}{25}, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{-\frac{8}{25}w}{-\frac{8}{25}}=\frac{4x\left(3x-325\right)}{-\frac{8}{25}\times 3125}$$

Dividing by -\frac{8}{25} undoes the multiplication by -\frac{8}{25}.

$$w=\frac{4x\left(3x-325\right)}{-\frac{8}{25}\times 3125}$$

Divide \frac{4x\left(-325+3x\right)}{3125} by -\frac{8}{25} by multiplying \frac{4x\left(-325+3x\right)}{3125} by the reciprocal of -\frac{8}{25}.

$$w=-\frac{3x^{2}}{250}+\frac{13x}{10}$$

Solve for x (complex solution)

$$x=\frac{-5\sqrt{4225-120w}+325}{6}$$

$$x=\frac{5\sqrt{4225-120w}+325}{6}$$

Solve for x

$$x=\frac{-5\sqrt{4225-120w}+325}{6}$$

$$x=\frac{5\sqrt{4225-120w}+325}{6}\text{, }w\leq \frac{845}{24}$$