Solve for x (x+2)(x+3)=x^2+5x+6

$(x + 2) (x + 3) = x^{2} + 5 x + 6$

Step 1

Simplify $(x + 2) (x + 3)$ .

Rewrite.

$0 + 0 + (x + 2) (x + 3) = x^{2} + 5 x + 6$

Simplify by adding zeros.

$(x + 2) (x + 3) = x^{2} + 5 x + 6$

Expand $(x + 2) (x + 3)$ using the FOIL Method.

Apply the distributive property.

$x (x + 3) + 2 (x + 3) = x^{2} + 5 x + 6$

Apply the distributive property.

$x \cdot x + x \cdot 3 + 2 (x + 3) = x^{2} + 5 x + 6$

Apply the distributive property.

$x \cdot x + x \cdot 3 + 2 x + 2 \cdot 3 = x^{2} + 5 x + 6$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + x \cdot 3 + 2 x + 2 \cdot 3 = x^{2} + 5 x + 6$

Move $3$ to the left of $x$ .

$x^{2} + 3 \cdot x + 2 x + 2 \cdot 3 = x^{2} + 5 x + 6$

Multiply $2$ by $3$ .

$x^{2} + 3 x + 2 x + 6 = x^{2} + 5 x + 6$

Add $3 x$ and $2 x$ .

$x^{2} + 5 x + 6 = x^{2} + 5 x + 6$

Step 2

Move all terms containing $x$ to the left side of the equation.

Subtract $x^{2}$ from both sides of the equation.

$x^{2} + 5 x + 6 - x^{2} = 5 x + 6$

Subtract $5 x$ from both sides of the equation.

$x^{2} + 5 x + 6 - x^{2} - 5 x = 6$

Combine the opposite terms in $x^{2} + 5 x + 6 - x^{2} - 5 x$ .

Subtract $x^{2}$ from $x^{2}$ .

$5 x + 6 + 0 - 5 x = 6$

Add $5 x + 6$ and $0$ .

$5 x + 6 - 5 x = 6$

Subtract $5 x$ from $5 x$ .

$0 + 6 = 6$

Add $0$ and $6$ .

$6 = 6$

Step 3

Since $6 = 6$ , the equation will always be true for any value of $x$ .

All real numbers

Step 4

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$

Solve for x (x+2)(x+3)=x^2+5x+6

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