Algebra Examples

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

Step 1

Since $x$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

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

Step 2

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

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Step 2.1

Subtract $x$ from both sides of the equation.

$x^{2} + 3 x - x = 3$

Step 2.2

Subtract $x$ from $3 x$ .

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

Step 3

Subtract $3$ from both sides of the equation.

$x^{2} + 2 x - 3 = 0$

Step 4

Factor $x^{2} + 2 x - 3$ using the AC method.

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Step 4.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 3$ and whose sum is $2$ .

$- 1, 3$

Step 4.2

Write the factored form using these integers.

$(x - 1) (x + 3) = 0$

Step 5

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x - 1 = 0$

$x + 3 = 0$

Step 6

Set $x - 1$ equal to $0$ and solve for $x$ .

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Step 6.1

Set $x - 1$ equal to $0$ .

$x - 1 = 0$

Step 6.2

Add $1$ to both sides of the equation.

$x = 1$

Step 7

Set $x + 3$ equal to $0$ and solve for $x$ .

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Step 7.1

Set $x + 3$ equal to $0$ .

$x + 3 = 0$

Step 7.2

Subtract $3$ from both sides of the equation.

$x = - 3$

Step 8

The final solution is all the values that make $(x - 1) (x + 3) = 0$ true.

$x = 1, - 3$

Step 9