Solve for x (x+4)(x-3)=-5x-11

$(x + 4) (x - 3) = - 5 x - 11$

Simplify $(x + 4) (x - 3)$ .

Rewrite.

$0 + 0 + (x + 4) (x - 3) = - 5 x - 11$

Simplify by adding zeros.

$(x + 4) (x - 3) = - 5 x - 11$

Expand $(x + 4) (x - 3)$ using the FOIL Method.

Apply the distributive property.

$x (x - 3) + 4 (x - 3) = - 5 x - 11$

Apply the distributive property.

$x \cdot x + x \cdot - 3 + 4 (x - 3) = - 5 x - 11$

Apply the distributive property.

$x \cdot x + x \cdot - 3 + 4 x + 4 \cdot - 3 = - 5 x - 11$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + x \cdot - 3 + 4 x + 4 \cdot - 3 = - 5 x - 11$

Move $- 3$ to the left of $x$ .

$x^{2} - 3 \cdot x + 4 x + 4 \cdot - 3 = - 5 x - 11$

Multiply $4$ by $- 3$ .

$x^{2} - 3 x + 4 x - 12 = - 5 x - 11$

Add $- 3 x$ and $4 x$ .

$x^{2} + x - 12 = - 5 x - 11$

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

Add $5 x$ to both sides of the equation.

$x^{2} + x - 12 + 5 x = - 11$

Add $x$ and $5 x$ .

$x^{2} + 6 x - 12 = - 11$

Move all terms to the left side of the equation and simplify.

Add $11$ to both sides of the equation.

$x^{2} + 6 x - 12 + 11 = 0$

Add $- 12$ and $11$ .

$x^{2} + 6 x - 1 = 0$

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Substitute the values $a = 1$ , $b = 6$ , and $c = - 1$ into the quadratic formula and solve for $x$ .

$\frac{- 6 \pm \sqrt{6^{2} - 4 \cdot (1 \cdot - 1)}}{2 \cdot 1}$

Simplify.

Simplify the numerator.

Raise $6$ to the power of $2$ .

$x = \frac{- 6 \pm \sqrt{36 - 4 \cdot 1 \cdot - 1}}{2 \cdot 1}$

Multiply $- 4$ by $1$ .

$x = \frac{- 6 \pm \sqrt{36 - 4 \cdot - 1}}{2 \cdot 1}$

Multiply $- 4$ by $- 1$ .

$x = \frac{- 6 \pm \sqrt{36 + 4}}{2 \cdot 1}$

Add $36$ and $4$ .

$x = \frac{- 6 \pm \sqrt{40}}{2 \cdot 1}$

Rewrite $40$ as $2^{2} \cdot 10$ .

Factor $4$ out of $40$ .

$x = \frac{- 6 \pm \sqrt{4 (10)}}{2 \cdot 1}$

Rewrite $4$ as $2^{2}$ .

$x = \frac{- 6 \pm \sqrt{2^{2} \cdot 10}}{2 \cdot 1}$

Pull terms out from under the radical.

$x = \frac{- 6 \pm 2 \sqrt{10}}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{- 6 \pm 2 \sqrt{10}}{2}$

Simplify $\frac{- 6 \pm 2 \sqrt{10}}{2}$ .

$x = - 3 \pm \sqrt{10}$

The final answer is the combination of both solutions.

$x = - 3 + \sqrt{10}, - 3 - \sqrt{10}$

The result can be shown in multiple forms.

Exact Form:

$x = - 3 + \sqrt{10}, - 3 - \sqrt{10}$

Decimal Form:

$x = 0.16227766 \dots, - 6.16227766 \dots$

Solve for x (x+4)(x-3)=-5x-11

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