Solve by Factoring x^2-13x+4=-6x-2

$x^{2} - 13 x + 4 = - 6 x - 2$

Step 1

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

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

$x^{2} - 13 x + 4 + 6 x = - 2$

Add $2$ to both sides of the equation.

$x^{2} - 13 x + 4 + 6 x + 2 = 0$

Step 2

Simplify $x^{2} - 13 x + 4 + 6 x + 2$ .

Add $- 13 x$ and $6 x$ .

$x^{2} - 7 x + 4 + 2 = 0$

Add $4$ and $2$ .

$x^{2} - 7 x + 6 = 0$

Step 3

Factor $x^{2} - 7 x + 6$ using the AC method.

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 $6$ and whose sum is $- 7$ .

$- 6, - 1$

Write the factored form using these integers.

$(x - 6) (x - 1) = 0$

Step 4

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

$x - 6 = 0$

$x - 1 = 0$

Step 5

Set $x - 6$ equal to $0$ and solve for $x$ .

Set $x - 6$ equal to $0$ .

$x - 6 = 0$

Add $6$ to both sides of the equation.

$x = 6$

Step 6

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

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

$x - 1 = 0$

Add $1$ to both sides of the equation.

$x = 1$

Step 7

The final solution is all the values that make $(x - 6) (x - 1) = 0$ true.

$x = 6, 1$

Solve by Factoring x^2-13x+4=-6x-2

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