Question

Resolver: 3x(x - 2) - 1 = 3(x + 2) (x + 4)​

Answer 1

Es una ecuacion que debemos aplicar

◘  Propiedad Distributiva

◘  Juntar los semejantes

◘ Despejar

◘ Resolver

Propiedad Distributiva

a(x+b) = a.x + a.b

entonces  

$3x(x - 2) - 1 = 3(x + 2) (x + 4)} \\\\ 3x.(x) - 3x.(2) - 1 = 3[(x).(x)+(x).(4) + 2.(x)+2.(4)]\to Propiedad \ Distributiva\\\\ 3x^2 - 6x - 1 = 3[x^2 + 4x + 2x + 8]\to Resolvimos \ y\ Prop. \ Distributiva\\\\ 3x^2 -6x - 1 = 3x^2 +12x +6x + 24 \to Juntamos\\\\ 3x^2 - 6x -3x^2 -12x - 6x = 24 + 1\to Resolvemos\\\\ 3x^2 -3x^2 - 24x= 25 \to Seguimos\ resolviendo\\\\ 3x^2 - 24x = 25\to Despejamos\\\\\\ x= -\dfrac{25}{24}\qquad\to Resultado \ negativo$

Verificamos

$3x(x - 2) - 1 = 3(x + 2) (x + 4)} \qquad\qquad x= -\dfrac{25}{24}\\\\\\ 3\left( -\dfrac{25}{24}\right). \left(\left( -\dfrac{25}{24}\right) - 2\right) - 1 = 3\left(\left( -\dfrac{25}{24}\right) + 2\right).\left (\left( -\dfrac{25}{24}\right) + 4\right)} \\\\\\ \left( -\dfrac{25}{8}\right). \left(\left( \dfrac{-25-48}{24}\right)\right) - 1 = 3\left(\left(\dfrac{-25+48}{24}\right) \right).\left (\left( \dfrac{-25+96}{24}\right)\right)}$

$\left( -\dfrac{25}{8}\right). \left(\left( \dfrac{-73}{24}\right)\right) - 1 = 3\left(\left(\dfrac{23}{24}\right) \right).\left (\left( \dfrac{71}{24}\right)\right)} \\\\\\ \left( +\dfrac{1825}{192}\right) - 1 = 3\left(\dfrac{1633}{576}\right)} \\\\\\ \dfrac{1825-192}{192} = \dfrac{4899}{576} \\\\\\ \dfrac{1633}{192} = \dfrac{4899}{576}\qquad simplificamos \\\\\\ \dfrac{1633}{192} = \dfrac{1633}{192}\qquad\checkmark$

Espero que te sirva, salu2!!!!