Finite Math Examples

$3 x^{2} - 5 x - 7 = - 2 x - 1$

Step 1

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

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Step 1.1

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

$3 x^{2} - 5 x - 7 + 2 x = - 1$

Step 1.2

Add $- 5 x$ and $2 x$ .

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

Step 2

Add $1$ to both sides of the equation.

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

Step 3

Add $- 7$ and $1$ .

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

Step 4

Factor the left side of the equation.

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Step 4.1

Factor $3$ out of $3 x^{2} - 3 x - 6$ .

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Step 4.1.1

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

$3 (x^{2}) - 3 x - 6 = 0$

Step 4.1.2

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

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

Step 4.1.3

Factor $3$ out of $- 6$ .

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

Step 4.1.4

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

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

Step 4.1.5

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

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

Step 4.2

Factor.

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Step 4.2.1

Factor $x^{2} - x - 2$ using the AC method.

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Step 4.2.1.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 2$ and whose sum is $- 1$ .

$- 2, 1$

Step 4.2.1.2

Write the factored form using these integers.

$3 ((x - 2) (x + 1)) = 0$

Step 4.2.2

Remove unnecessary parentheses.

$3 (x - 2) (x + 1) = 0$

Step 5

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

$x - 2 = 0$

$x + 1 = 0$

Step 6

Set $x - 2$ equal to $0$ and solve for $x$ .

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Step 6.1

Set $x - 2$ equal to $0$ .

$x - 2 = 0$

Step 6.2

Add $2$ to both sides of the equation.

$x = 2$

Step 7

Set $x + 1$ equal to $0$ and solve for $x$ .

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Step 7.1

Set $x + 1$ equal to $0$ .

$x + 1 = 0$

Step 7.2

Subtract $1$ from both sides of the equation.

$x = - 1$

Step 8

The final solution is all the values that make $3 (x - 2) (x + 1) = 0$ true.

$x = 2, - 1$