Solve the Cubic Equation: x³ + x² - 12x = 0

Question

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

00:00 Find X

00:03 Factor with factor X

00:14 Take out the common factor from parentheses

00:31 This is one solution that zeros the equation

00:37 Now let's solve the second factor

00:44 Factor using trinomial, identify coefficients

00:48 We want to find 2 numbers whose sum equals B (1)

00:54 And their product equals C (-12)

01:00 These are the matching numbers, let's substitute in parentheses

01:05 Find what zeros each factor

01:10 And this is the solution to the question

To solve the equation $x^3 + x^2 - 12x = 0$ , follow these steps:

Step 1: Factor out the greatest common factor. The common factor here is $x$ .
Step 2: The equation becomes $x(x^2 + x - 12) = 0$ .
Step 3: Apply the zero-product property. This gives us two equations to solve: $x = 0$ and $x^2 + x - 12 = 0$ .
Step 4: Solve $x = 0$ . This is a straightforward solution: $x = 0$ .
Step 5: Solve the quadratic equation $x^2 + x - 12 = 0$ . We will factor it:

Therefore, the solutions to the equation are $x = 0$ , $x = 3$ , and $x = -4$ .

Thus, the complete solution set for $x$ is $x = 0, 3, -4$ .

$x=0,3,-4$