Solve 25/4=-(3/2-x)(3/2-4)

$$\frac{ 25 }{ 4 } =-( \frac{ 3 }{ 2 } -x)( \frac{ 3 }{ 2 } -4)$$

Solve for x

$$x=-1$$

Steps for Solving Linear Equation

To find the opposite of \frac{3}{2}-x, find the opposite of each term.

$$\frac{25}{4}=\left(-\frac{3}{2}-\left(-x\right)\right)\left(\frac{3}{2}-4\right)$$

The opposite of -x is x.

$$\frac{25}{4}=\left(-\frac{3}{2}+x\right)\left(\frac{3}{2}-4\right)$$

Convert 4 to fraction \frac{8}{2}.

$$\frac{25}{4}=\left(-\frac{3}{2}+x\right)\left(\frac{3}{2}-\frac{8}{2}\right)$$

Since \frac{3}{2} and \frac{8}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{25}{4}=\left(-\frac{3}{2}+x\right)\times \frac{3-8}{2}$$

Subtract 8 from 3 to get -5.

$$\frac{25}{4}=\left(-\frac{3}{2}+x\right)\left(-\frac{5}{2}\right)$$

Use the distributive property to multiply -\frac{3}{2}+x by -\frac{5}{2}.

$$\frac{25}{4}=-\frac{3}{2}\left(-\frac{5}{2}\right)+x\left(-\frac{5}{2}\right)$$

Multiply -\frac{3}{2} times -\frac{5}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{25}{4}=\frac{-3\left(-5\right)}{2\times 2}+x\left(-\frac{5}{2}\right)$$

Do the multiplications in the fraction \frac{-3\left(-5\right)}{2\times 2}.

$$\frac{25}{4}=\frac{15}{4}+x\left(-\frac{5}{2}\right)$$

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

$$\frac{15}{4}+x\left(-\frac{5}{2}\right)=\frac{25}{4}$$

Subtract \frac{15}{4} from both sides.

$$x\left(-\frac{5}{2}\right)=\frac{25}{4}-\frac{15}{4}$$

Since \frac{25}{4} and \frac{15}{4} have the same denominator, subtract them by subtracting their numerators.

$$x\left(-\frac{5}{2}\right)=\frac{25-15}{4}$$

Subtract 15 from 25 to get 10.

$$x\left(-\frac{5}{2}\right)=\frac{10}{4}$$

Reduce the fraction \frac{10}{4} to lowest terms by extracting and canceling out 2.

$$x\left(-\frac{5}{2}\right)=\frac{5}{2}$$

Multiply both sides by -\frac{2}{5}, the reciprocal of -\frac{5}{2}.

$$x=\frac{5}{2}\left(-\frac{2}{5}\right)$$

Multiply \frac{5}{2} times -\frac{2}{5} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{5\left(-2\right)}{2\times 5}$$

Cancel out 5 in both numerator and denominator.

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

Divide -2 by 2 to get -1.

$$x=-1$$