Algebra Examples

$- x^{2} + 10 x = x^{2} - 6 x$

Step 1

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

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Step 1.1

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

$- x^{2} + 10 x - x^{2} = - 6 x$

Step 1.2

Add $6 x$ to both sides of the equation.

$- x^{2} + 10 x - x^{2} + 6 x = 0$

Step 1.3

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

$- 2 x^{2} + 10 x + 6 x = 0$

Step 1.4

Add $10 x$ and $6 x$ .

$- 2 x^{2} + 16 x = 0$

Step 2

Factor $- 2 x$ out of $- 2 x^{2} + 16 x$ .

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Step 2.1

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

$- 2 x \cdot x + 16 x = 0$

Step 2.2

Factor $- 2 x$ out of $16 x$ .

$- 2 x \cdot x - 2 x \cdot - 8 = 0$

Step 2.3

Factor $- 2 x$ out of $- 2 x (x) - 2 x (- 8)$ .

$- 2 x (x - 8) = 0$

Step 3

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

$x = 0$

$x - 8 = 0$

Step 4

Set $x$ equal to $0$ .

$x = 0$

Step 5

Set $x - 8$ equal to $0$ and solve for $x$ .

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Step 5.1

Set $x - 8$ equal to $0$ .

$x - 8 = 0$

Step 5.2

Add $8$ to both sides of the equation.

$x = 8$

Step 6

The final solution is all the values that make $- 2 x (x - 8) = 0$ true.

$x = 0, 8$