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

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

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

We move all terms to the left:

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

We multiply parentheses

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


We calculate terms in parentheses: -(-2(4x+3)), so:

-2(4x+3)

We multiply parentheses

-8x-6

Back to the equation:

-(-8x-6)


We get rid of parentheses

-8x^2-12x+8x+6=0

We add all the numbers together, and all the variables

-8x^2-4x+6=0

a = -8; b = -4; c = +6;
Δ = b2-4ac
Δ = -42-4·(-8)·6
Δ = 208
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{208}=\sqrt{16*13}=\sqrt{16}*\sqrt{13}=4\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{13}}{2*-8}=\frac{4-4\sqrt{13}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{13}}{2*-8}=\frac{4+4\sqrt{13}}{-16}
$