${\left( 10c-9 \right)}^{2}-{12}^{2}=0$
Use ${\left( a-b \right)}^{2}={a}^{2}-2ab+{b}^{2}$ to expand the expression$100{c}^{2}-180c+81-{12}^{2}=0$
Evaluate the power$100{c}^{2}-180c+81-144=0$
Write $-180c$ as a difference$100{c}^{2}+30c-210c+81-144=0$
Calculate the difference$100{c}^{2}+30c-210c-63=0$
Factor out $10c$ from the expression$10c \times \left( 10c+3 \right)-210c-63=0$
Factor out $-21$ from the expression$10c \times \left( 10c+3 \right)-21\left( 10c+3 \right)=0$
Factor out $10c+3$ from the expression$\left( 10c+3 \right) \times \left( 10c-21 \right)=0$
When the product of factors equals $0$, at least one factor is $0$$\begin{array} { l }10c+3=0,\\10c-21=0\end{array}$
Solve the equation for $c$$\begin{array} { l }c=-\frac{ 3 }{ 10 },\\10c-21=0\end{array}$
Solve the equation for $c$$\begin{array} { l }c=-\frac{ 3 }{ 10 },\\c=\frac{ 21 }{ 10 }\end{array}$
The equation has $2$ solutions$\begin{align*}&\begin{array} { l }c_1=-\frac{ 3 }{ 10 },& c_2=\frac{ 21 }{ 10 }\end{array} \\&\begin{array} { l }c_1=-0.3,& c_2=2.1\end{array}\end{align*}$