Algebra Examples

$4 x^{5} - 12 x^{4} + 6 x = 5 x^{3} - 2 x$

Step 1

Move all the expressions to the left side of the equation.

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Step 1.1

Subtract $5 x^{3}$ from both sides of the equation.

$4 x^{5} - 12 x^{4} + 6 x - 5 x^{3} = - 2 x$

Step 1.2

Add $2 x$ to both sides of the equation.

$4 x^{5} - 12 x^{4} + 6 x - 5 x^{3} + 2 x = 0$

Step 2

Add $6 x$ and $2 x$ .

$4 x^{5} - 12 x^{4} - 5 x^{3} + 8 x = 0$

Step 3

Factor $x$ out of $4 x^{5} - 12 x^{4} - 5 x^{3} + 8 x$ .

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Step 3.1

Factor $x$ out of $4 x^{5}$ .

$x (4 x^{4}) - 12 x^{4} - 5 x^{3} + 8 x = 0$

Step 3.2

Factor $x$ out of $- 12 x^{4}$ .

$x (4 x^{4}) + x (- 12 x^{3}) - 5 x^{3} + 8 x = 0$

Step 3.3

Factor $x$ out of $- 5 x^{3}$ .

$x (4 x^{4}) + x (- 12 x^{3}) + x (- 5 x^{2}) + 8 x = 0$

Step 3.4

Factor $x$ out of $8 x$ .

$x (4 x^{4}) + x (- 12 x^{3}) + x (- 5 x^{2}) + x \cdot 8 = 0$

Step 3.5

Factor $x$ out of $x (4 x^{4}) + x (- 12 x^{3})$ .

$x (4 x^{4} - 12 x^{3}) + x (- 5 x^{2}) + x \cdot 8 = 0$

Step 3.6

Factor $x$ out of $x (4 x^{4} - 12 x^{3}) + x (- 5 x^{2})$ .

$x (4 x^{4} - 12 x^{3} - 5 x^{2}) + x \cdot 8 = 0$

Step 3.7

Factor $x$ out of $x (4 x^{4} - 12 x^{3} - 5 x^{2}) + x \cdot 8$ .

$x (4 x^{4} - 12 x^{3} - 5 x^{2} + 8) = 0$