Algebra Examples

$7 x + 1 = 3 x^{2} - 2 x + 1$

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.

$3 x^{2} - 2 x + 1 = 7 x + 1$

Step 2

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

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Step 2.1

Subtract $7 x$ from both sides of the equation.

$3 x^{2} - 2 x + 1 - 7 x = 1$

Step 2.2

Subtract $7 x$ from $- 2 x$ .

$3 x^{2} - 9 x + 1 = 1$

Step 3

Subtract $1$ from both sides of the equation.

$3 x^{2} - 9 x + 1 - 1 = 0$

Step 4

Combine the opposite terms in $3 x^{2} - 9 x + 1 - 1$ .

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Step 4.1

Subtract $1$ from $1$ .

$3 x^{2} - 9 x + 0 = 0$

Step 4.2

Add $3 x^{2} - 9 x$ and $0$ .

$3 x^{2} - 9 x = 0$

Step 5

Factor $3 x$ out of $3 x^{2} - 9 x$ .

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Step 5.1

Factor $3 x$ out of $3 x^{2}$ .

$3 x (x) - 9 x = 0$

Step 5.2

Factor $3 x$ out of $- 9 x$ .

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

Step 5.3

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

$3 x (x - 3) = 0$

Step 6

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 7

Set $x$ equal to $0$ .

$x = 0$

Step 8

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

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Step 8.1

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

$x - 3 = 0$

Step 8.2

Add $3$ to both sides of the equation.

$x = 3$

Step 9

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

$x = 0, 3$