(x-4)(2x+3)=-3(x-4)

Solution for (x-4)(2x+3)=-3(x-4) equation:

(x-4)(2x+3)=-3(x-4)

We move all terms to the left:

(x-4)(2x+3)-(-3(x-4))=0

We multiply parentheses ..

(+2x^2+3x-8x-12)-(-3(x-4))=0


We calculate terms in parentheses: -(-3(x-4)), so:

-3(x-4)

We multiply parentheses

-3x+12

Back to the equation:

-(-3x+12)


We get rid of parentheses

2x^2+3x-8x+3x-12-12=0

We add all the numbers together, and all the variables

2x^2-2x-24=0

a = 2; b = -2; c = -24;
Δ = b2-4ac
Δ = -22-4·2·(-24)
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-14}{2*2}=\frac{-12}{4}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+14}{2*2}=\frac{16}{4}
=4
$