Solve the equation: (x+2)(x+3)=1-x

Solve the equation: (x+2)(x+3)=1–x.

STEP 1:    To solve the given equation means to find the values of x that satisfy the equation. As you can see, the left side of the equation contains linear factors. So, the first step that you need to do is to remove the parentheses, or you can say, expand the factors.

See how we can clear the parentheses by multiplying the terms.
removing the brackets (parentheses)

STEP 2:    What you need to do next is to rewrite the equation in the standard form. This will be helpful to check if we can solve the equation by factoring.

Subtract 1 and add x to each side of the equation.
simplifying the equation
STEP 3:    Now, you have a trinomial in the left, which can be factored.
factoring the quadratic equation
Now, we have to recall the zero-product property. By this, if a product of factors is equal to zero, then any of the factors or all factors must be equal to 0.
finding the value of x

Solve the equations separately for x.
possible values of x
You finally get the solutions of the given equation as:

                            x = –1 and x = –5.

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