# Solve Equations with Decimal Coefficients In the following exercises, solve the equation 0.10d+0.25(d+5)=4.05

Solve Equations with Decimal Coefficients In the following exercises, solve the equation by clearing the decimals.
$$\displaystyle{0.10}{d}+{0.25}{\left({d}+{5}\right)}={4.05}$$

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Step 1
The given equation is $$\displaystyle{0.10}{d}+{0.25}{\left({d}+{5}\right)}={4.05}$$
The equation $$\displaystyle{0.10}{d}+{0.25}{\left({d}+{5}\right)}={4.05}$$ can be solved as follows.
Wemultiply the decimal number by 100 to shift the decimal towards right hand side by two place.
Step 2
For clearing the decimals we multiply each term by 100.
$$\displaystyle\Rightarrow{100}\times{0.10}{d}+{100}\times{0.25}{\left({d}+{5}\right)}={100}\times{4.05}$$
$$\displaystyle\Rightarrow{10}{d}+{25}{\left({d}+{5}\right)}={405}$$
$$\displaystyle\Rightarrow{10}{d}+{25}{d}+{125}={405}$$
Subtract 125 on sides.
$$\displaystyle\Rightarrow{10}{d}+{25}{d}+{125}-{125}={405}-{125}$$
$$\displaystyle\Rightarrow{35}{d}={280}$$
Divide both sides by 35.
$$\displaystyle\Rightarrow{\frac{{{35}{d}}}{{{35}}}}={\frac{{{280}}}{{{35}}}}$$
$$\displaystyle\Rightarrow\ {d}={8}$$
Therefore, $$\displaystyle{d}={8}$$ is the solution of $$\displaystyle{0.10}{d}+{0.25}{\left({d}+{5}\right)}={4.05}.$$