Solve 0=2/3125H+10left(12.5H+26*417-93.75right)

$$0 = \frac{ 2 }{ 3 } 125H+10 \left( 12.5H+26 \cdot 417-93.75 \right)$$

Solve for H

$$H=-515.916$$

Steps for Solving Linear Equation

Express \frac{2}{3}\times 125 as a single fraction.

$$0=\frac{2\times 125}{3}H+10\left(12.5H+26\times 417-93.75\right)$$

Multiply 2 and 125 to get 250.

$$0=\frac{250}{3}H+10\left(12.5H+26\times 417-93.75\right)$$

Multiply 26 and 417 to get 10842.

$$0=\frac{250}{3}H+10\left(12.5H+10842-93.75\right)$$

Subtract 93.75 from 10842 to get 10748.25.

$$0=\frac{250}{3}H+10\left(12.5H+10748.25\right)$$

Use the distributive property to multiply 10 by 12.5H+10748.25.

$$0=\frac{250}{3}H+125H+107482.5$$

Combine \frac{250}{3}H and 125H to get \frac{625}{3}H.

$$0=\frac{625}{3}H+107482.5$$

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

$$\frac{625}{3}H+107482.5=0$$

Subtract 107482.5 from both sides. Anything subtracted from zero gives its negation.

$$\frac{625}{3}H=-107482.5$$

Multiply both sides by \frac{3}{625}, the reciprocal of \frac{625}{3}.

$$H=-107482.5\times \frac{3}{625}$$

Convert decimal number -107482.5 to fraction -\frac{1074825}{10}. Reduce the fraction -\frac{1074825}{10} to lowest terms by extracting and canceling out 5.

$$H=-\frac{214965}{2}\times \frac{3}{625}$$

Multiply -\frac{214965}{2} times \frac{3}{625} by multiplying numerator times numerator and denominator times denominator.

$$H=\frac{-214965\times 3}{2\times 625}$$

Do the multiplications in the fraction \frac{-214965\times 3}{2\times 625}.

$$H=\frac{-644895}{1250}$$

Reduce the fraction \frac{-644895}{1250} to lowest terms by extracting and canceling out 5.

$$H=-\frac{128979}{250}$$