Calculus Examples

$x^{2} - 4 x + 3 = - x^{2} + 2 x + 3$

Step 1

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

Tap for more steps...

Step 1.1

Add $x^{2}$ to both sides of the equation.

$x^{2} - 4 x + 3 + x^{2} = 2 x + 3$

Step 1.2

Subtract $2 x$ from both sides of the equation.

$x^{2} - 4 x + 3 + x^{2} - 2 x = 3$

Step 1.3

Add $x^{2}$ and $x^{2}$ .

$2 x^{2} - 4 x + 3 - 2 x = 3$

Step 1.4

Subtract $2 x$ from $- 4 x$ .

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

Step 2

Subtract $3$ from both sides of the equation.

$2 x^{2} - 6 x + 3 - 3 = 0$

Step 3

Combine the opposite terms in $2 x^{2} - 6 x + 3 - 3$ .

Tap for more steps...

Step 3.1

Subtract $3$ from $3$ .

$2 x^{2} - 6 x + 0 = 0$

Step 3.2

Add $2 x^{2} - 6 x$ and $0$ .

$2 x^{2} - 6 x = 0$

Step 4

Factor $2 x$ out of $2 x^{2} - 6 x$ .

Tap for more steps...

Step 4.1

Factor $2 x$ out of $2 x^{2}$ .

$2 x (x) - 6 x = 0$

Step 4.2

Factor $2 x$ out of $- 6 x$ .

$2 x (x) + 2 x (- 3) = 0$

Step 4.3

Factor $2 x$ out of $2 x (x) + 2 x (- 3)$ .

$2 x (x - 3) = 0$

Step 5

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

$x = 0$

$x - 3 = 0$

Step 6

Set $x$ equal to $0$ .

$x = 0$

Step 7

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

Tap for more steps...

Step 7.1

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

$x - 3 = 0$

Step 7.2

Add $3$ to both sides of the equation.

$x = 3$

Step 8

The final solution is all the values that make $2 x (x - 3) = 0$ true.

$x = 0, 3$