Algebra Examples

$147 x - 49 = 3 x^{3} - x^{2}$

Step 1

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

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Step 1.1

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

$147 x - 49 - 3 x^{3} = - x^{2}$

Step 1.2

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

$147 x - 49 - 3 x^{3} + x^{2} = 0$

Step 2

Factor the left side.

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Step 2.1

Reorder terms.

$- 3 x^{3} + x^{2} + 147 x - 49 = 0$

Step 2.2

Factor out the greatest common factor from each group.

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Step 2.2.1

Group the first two terms and the last two terms.

$(- 3 x^{3} + x^{2}) + 147 x - 49 = 0$

Step 2.2.2

Factor out the greatest common factor (GCF) from each group.

$x^{2} (- 3 x + 1) - 49 (- 3 x + 1) = 0$

Step 2.3

Factor the polynomial by factoring out the greatest common factor, $- 3 x + 1$ .

$(- 3 x + 1) (x^{2} - 49) = 0$

Step 2.4

Rewrite $49$ as $7^{2}$ .

$(- 3 x + 1) (x^{2} - 7^{2}) = 0$

Step 2.5

Factor.

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Step 2.5.1

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = 7$ .

$(- 3 x + 1) ((x + 7) (x - 7)) = 0$

Step 2.5.2

Remove unnecessary parentheses.

$(- 3 x + 1) (x + 7) (x - 7) = 0$