Solve (x + 2)(x - 3) = x ^ 2 - kx - 6 | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

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

Solve for k (complex solution)

$\left\{\begin{matrix}\\k=1\text{, }&\text{unconditionally}\\k\in \mathrm{C}\text{, }&x=0\end{matrix}\right.$

Steps for Solving Linear Equation

Use the distributive property to multiply $x+2$ by $x-3$ and combine like terms.

$$x^{2}-x-6=x^{2}-kx-6$$

Swap sides so that all variable terms are on the left hand side.

$$x^{2}-kx-6=x^{2}-x-6$$

Subtract $x^{2}$ from both sides.

$$-kx-6=x^{2}-x-6-x^{2}$$

Combine $x^{2}$ and $-x^{2}$ to get $0$.

$$-kx-6=-x-6$$

Add $6$ to both sides.

$$-kx=-x-6+6$$

Add $-6$ and $6$ to get $0$.

$$-kx=-x$$

Cancel out $-1$ on both sides.

$$kx=x$$

The equation is in standard form.

$$xk=x$$

Divide both sides by $x$.

$$\frac{xk}{x}=\frac{x}{x}$$

Dividing by $x$ undoes the multiplication by $x$.

$$k=\frac{x}{x}$$

Divide $x$ by $x$.

$$k=1$$

Solve for x (complex solution)

$\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x\in \mathrm{C}\text{, }&k=1\end{matrix}\right.$

Steps for Solving Linear Equation

Use the distributive property to multiply $x+2$ by $x-3$ and combine like terms.

$$x^{2}-x-6=x^{2}-kx-6$$

Subtract $x^{2}$ from both sides.

$$x^{2}-x-6-x^{2}=-kx-6$$

Combine $x^{2}$ and $-x^{2}$ to get $0$.

$$-x-6=-kx-6$$

Add $kx$ to both sides.

$$-x-6+kx=-6$$

Add $6$ to both sides.

$$-x+kx=-6+6$$

Add $-6$ and $6$ to get $0$.

$$-x+kx=0$$

Combine all terms containing $x$.

$$\left(-1+k\right)x=0$$

The equation is in standard form.

$$\left(k-1\right)x=0$$

Divide $0$ by $-1+k$.

$$x=0$$

Solve for k

$\left\{\begin{matrix}\\k=1\text{, }&\text{unconditionally}\\k\in \mathrm{R}\text{, }&x=0\end{matrix}\right.$

Steps for Solving Linear Equation

Use the distributive property to multiply $x+2$ by $x-3$ and combine like terms.

$$x^{2}-x-6=x^{2}-kx-6$$

Swap sides so that all variable terms are on the left hand side.

$$x^{2}-kx-6=x^{2}-x-6$$

Subtract $x^{2}$ from both sides.

$$-kx-6=x^{2}-x-6-x^{2}$$

Combine $x^{2}$ and $-x^{2}$ to get $0$.

$$-kx-6=-x-6$$

Add $6$ to both sides.

$$-kx=-x-6+6$$

Add $-6$ and $6$ to get $0$.

$$-kx=-x$$

Cancel out $-1$ on both sides.

$$kx=x$$

The equation is in standard form.

$$xk=x$$

Divide both sides by $x$.

$$\frac{xk}{x}=\frac{x}{x}$$

Dividing by $x$ undoes the multiplication by $x$.

$$k=\frac{x}{x}$$

Divide $x$ by $x$.

$$k=1$$

Solve for x

$\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x\in \mathrm{R}\text{, }&k=1\end{matrix}\right.$

Steps for Solving Linear Equation

Use the distributive property to multiply $x+2$ by $x-3$ and combine like terms.

$$x^{2}-x-6=x^{2}-kx-6$$

Subtract $x^{2}$ from both sides.

$$x^{2}-x-6-x^{2}=-kx-6$$

Combine $x^{2}$ and $-x^{2}$ to get $0$.

$$-x-6=-kx-6$$

Add $kx$ to both sides.

$$-x-6+kx=-6$$

Add $6$ to both sides.

$$-x+kx=-6+6$$

Add $-6$ and $6$ to get $0$.

$$-x+kx=0$$

Combine all terms containing $x$.

$$\left(-1+k\right)x=0$$

The equation is in standard form.

$$\left(k-1\right)x=0$$

Divide $0$ by $-1+k$.

$$x=0$$