Question

(5x-2)(x+1)=3x(3x-1)solve by factorization method

Answer 1

$Given \:(5x-2)(x+1) = 3x(3x-1)$

$\implies 5x(x+1)-2(x+1) = 9x^{2} - 3x$

$\implies 5x^{2} + 5x - 2x - 2 = 9x^{2} - 3x$

$\implies 5x^{2} + 3x - 2 = 9x^{2} - 3x$

$\implies 0 = - 5x^{2} - 3x + 2 + 9x^{2} - 3x$

$\implies 4x^{2} - 6x + 2 = 0$

$\implies 4x^{2} - 4x - 2x + 2 = 0$

$\implies 4x( x - 1 ) - 2( x - 1 ) = 0$

$\implies (x-1)(4x-2) = 0$

$\implies x-1 = 0 \:Or \: 4x-2= 0$

$\implies x = 1 \:Or \: 4x = 2$

$\implies x = 1 \:Or \: x = \frac{2}{4}$

$\implies x = 1 \:Or \: x = \frac{1}{2}$

Therefore.,

$\green { 1 \:and \: \frac{1}{2}\: are \: roots \: of }$

$\green { the \: equation }$

•••♪