How do you solve $3(4 - x)(2x + 1) = 0$ ?

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Answer 1 · 2017-05-15T21:56:19

See a solution process below:

First, divide each side of the equation by $color(red)(3)$ to eliminate the constant while keeping the equation balanced"

$(3(4 - x)(2x + 1))/color(red)(3) = 0/color(red)(3)$

$(color(red)(cancel(color(black)(3)))(4 - x)(2x + 1))/cancel(color(red)(3)) = 0$

$(4 - x)(2x + 1) = 0$

Solve each term on the left side of the equation for $0$ :

Solution 1)

$4 - x = 0$

$-color(red)(4) + 4 - x = -color(red)(4) + 0$

$0 - x = -4$

$-x = -4$

$color(red)(-1) xx -x = color(red)(-1) xx -4$

$x = 4$

Solution 2)

$2x + 1 = 0$

$2x + 1 - color(red)(1) = 0 - color(red)(1)$

$2x + 0 = -1$

$2x = -1$

$(2x)/color(red)(2) = -1/color(red)(2)$

$(color(red)(cancel(color(black)(2)))x)/cancel(color(red)(2)) = -1/2$

$x = -1/2$

The solutions are: $x = 4$ and $x = -1/2$

How do you solve 3(4 - x)(2x + 1) = 03(4 - x)(2x + 1) = 0?