(m-5)(m+2)=(m+2)

Solution for (m-5)(m+2)=(m+2) equation:

(m-5)(m+2)=(m+2)

We move all terms to the left:

(m-5)(m+2)-((m+2))=0

We multiply parentheses ..

(+m^2+2m-5m-10)-((m+2))=0


We calculate terms in parentheses: -((m+2)), so:

(m+2)

We get rid of parentheses

m+2

Back to the equation:

-(m+2)


We get rid of parentheses

m^2+2m-5m-m-10-2=0

We add all the numbers together, and all the variables

m^2-4m-12=0

a = 1; b = -4; c = -12;
Δ = b2-4ac
Δ = -42-4·1·(-12)
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-8}{2*1}=\frac{-4}{2}
=-2
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+8}{2*1}=\frac{12}{2}
=6
$