Solve for: (x-4) * (x+6)=11

Expression: $\left( x-4 \right) \times \left( x+6 \right)=11$

Simplify the expression

${x}^{2}+6x-4x-24=11$

Collect like terms

${x}^{2}+2x-24=11$

Move the constant to the left-hand side and change its sign

${x}^{2}+2x-24-11=0$

Calculate the difference

${x}^{2}+2x-35=0$

Identify the coefficients $p$ and $q$ of the quadratic equation

$\begin{array} { l }p=2,& q=-35\end{array}$

Substitute $p=2$ and $q=-35$ into the PQ formula $x=-\frac{ p }{ 2 }\pm\sqrt{ {\left( \frac{ p }{ 2 } \right)}^{2}-q }$

$x=-\frac{ 2 }{ 2 }\pm\sqrt{ {\left( \frac{ 2 }{ 2 } \right)}^{2}-\left( -35 \right) }$

Any expression divided by itself equals $1$

$x=-1\pm\sqrt{ {\left( \frac{ 2 }{ 2 } \right)}^{2}-\left( -35 \right) }$

Simplify the expression

$x=-1\pm6$

Write the solutions, one with a $+$ sign and one with a $-$ sign

$\begin{array} { l }x=-1+6,\\x=-1-6\end{array}$

Calculate the sum

$\begin{array} { l }x=5,\\x=-1-6\end{array}$

Calculate the difference

$\begin{array} { l }x=5,\\x=-7\end{array}$

The equation has $2$ solutions

$\begin{array} { l }x_1=-7,& x_2=5\end{array}$