(5m+4)(m-2)=-2m(m+16)-27

Solution for (5m+4)(m-2)=-2m(m+16)-27 equation:

(5m+4)(m-2)=-2m(m+16)-27

We move all terms to the left:

(5m+4)(m-2)-(-2m(m+16)-27)=0

We multiply parentheses ..

(+5m^2-10m+4m-8)-(-2m(m+16)-27)=0


We calculate terms in parentheses: -(-2m(m+16)-27), so:

-2m(m+16)-27

We multiply parentheses

-2m^2-32m-27

Back to the equation:

-(-2m^2-32m-27)


We get rid of parentheses

5m^2+2m^2-10m+4m+32m-8+27=0

We add all the numbers together, and all the variables

7m^2+26m+19=0

a = 7; b = 26; c = +19;
Δ = b2-4ac
Δ = 262-4·7·19
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-12}{2*7}=\frac{-38}{14}
=-2+5/7
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+12}{2*7}=\frac{-14}{14}
=-1
$