$36{m}^{2}+12m+1-5\left( 6m+1 \right)+4=0$
Distribute $-5$ through the parentheses$36{m}^{2}+12m+1-30m-5+4=0$
Collect like terms$36{m}^{2}-18m+1-5+4=0$
Calculate the sum or difference$36{m}^{2}-18m+0=0$
Removing $0$ doesn't change the value, so remove it from the expression$36{m}^{2}-18m=0$
Write the quadratic equation in the appropriate form${m}^{2}-\frac{ 1 }{ 2 }m=0$
Identify the coefficients $p$ and $q$ of the quadratic equation$\begin{array} { l }p=-\frac{ 1 }{ 2 },& q=0\end{array}$
Substitute $p=-\frac{ 1 }{ 2 }$ and $q=0$ into the PQ formula $x=-\frac{ p }{ 2 }\pm\sqrt{ {\left( \frac{ p }{ 2 } \right)}^{2}-q }$$m=-\frac{ -\frac{ 1 }{ 2 } }{ 2 }\pm\sqrt{ {\left( \frac{ -\frac{ 1 }{ 2 } }{ 2 } \right)}^{2}-0 }$
Removing $0$ doesn't change the value, so remove it from the expression$m=-\frac{ -\frac{ 1 }{ 2 } }{ 2 }\pm\sqrt{ {\left( \frac{ -\frac{ 1 }{ 2 } }{ 2 } \right)}^{2} }$
Determine the sign of the fraction$m=\frac{ \frac{ 1 }{ 2 } }{ 2 }\pm\sqrt{ {\left( \frac{ -\frac{ 1 }{ 2 } }{ 2 } \right)}^{2} }$
Use $\frac{ -a }{ b }=\frac{ a }{ -b }=-\frac{ a }{ b }$ to rewrite the fraction$m=\frac{ \frac{ 1 }{ 2 } }{ 2 }\pm\sqrt{ {\left( -\frac{ \frac{ 1 }{ 2 } }{ 2 } \right)}^{2} }$
Simplify the complex fraction$m=\frac{ 1 }{ 4 }\pm\sqrt{ {\left( -\frac{ \frac{ 1 }{ 2 } }{ 2 } \right)}^{2} }$
Simplify the complex fraction$m=\frac{ 1 }{ 4 }\pm\sqrt{ {\left( -\frac{ 1 }{ 4 } \right)}^{2} }$
Reduce the index of the radical and exponent with $2$$m=\frac{ 1 }{ 4 }\pm\frac{ 1 }{ 4 }$
Write the solutions, one with a $+$ sign and one with a $-$ sign$\begin{array} { l }m=\frac{ 1 }{ 4 }+\frac{ 1 }{ 4 },\\m=\frac{ 1 }{ 4 }-\frac{ 1 }{ 4 }\end{array}$
Add the fractions$\begin{array} { l }m=\frac{ 1 }{ 2 },\\m=\frac{ 1 }{ 4 }-\frac{ 1 }{ 4 }\end{array}$
Subtract the fractions$\begin{array} { l }m=\frac{ 1 }{ 2 },\\m=0\end{array}$
The equation has $2$ solutions$\begin{align*}&\begin{array} { l }m_1=0,& m_2=\frac{ 1 }{ 2 }\end{array} \\&\begin{array} { l }m_1=0,& m_2=0.5\end{array}\end{align*}$