Solve (x+3)(x-1)=2x(x-2)+5

$$(x+3)(x-1)=2x(x-2)+5$$

Solve for x

$$x=2$$

$$x=4$$

Steps Using the Quadratic Formula

Use the distributive property to multiply x+3 by x-1 and combine like terms.

$$x^{2}+2x-3=2x\left(x-2\right)+5$$

Use the distributive property to multiply 2x by x-2.

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

Subtract 2x^{2} from both sides.

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

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

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

Add 4x to both sides.

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

Combine 2x and 4x to get 6x.

$$-x^{2}+6x-3=5$$

Subtract 5 from both sides.

$$-x^{2}+6x-3-5=0$$

Subtract 5 from -3 to get -8.

$$-x^{2}+6x-8=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -1 for a, 6 for b, and -8 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-6±\sqrt{6^{2}-4\left(-1\right)\left(-8\right)}}{2\left(-1\right)}$$

Square 6.

$$x=\frac{-6±\sqrt{36-4\left(-1\right)\left(-8\right)}}{2\left(-1\right)}$$

Multiply -4 times -1.

$$x=\frac{-6±\sqrt{36+4\left(-8\right)}}{2\left(-1\right)}$$

Multiply 4 times -8.

$$x=\frac{-6±\sqrt{36-32}}{2\left(-1\right)}$$

Add 36 to -32.

$$x=\frac{-6±\sqrt{4}}{2\left(-1\right)}$$

Take the square root of 4.

$$x=\frac{-6±2}{2\left(-1\right)}$$

Multiply 2 times -1.

$$x=\frac{-6±2}{-2}$$

Now solve the equation x=\frac{-6±2}{-2} when ± is plus. Add -6 to 2.

$$x=-\frac{4}{-2}$$

Divide -4 by -2.

$$x=2$$

Now solve the equation x=\frac{-6±2}{-2} when ± is minus. Subtract 2 from -6.

$$x=-\frac{8}{-2}$$

Divide -8 by -2.

$$x=4$$

The equation is now solved.

$$x=2 x=4$$

Steps for Completing the Square

Use the distributive property to multiply x+3 by x-1 and combine like terms.

$$x^{2}+2x-3=2x\left(x-2\right)+5$$

Use the distributive property to multiply 2x by x-2.

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

Subtract 2x^{2} from both sides.

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

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

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

Add 4x to both sides.

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

Combine 2x and 4x to get 6x.

$$-x^{2}+6x-3=5$$

Add 3 to both sides.

$$-x^{2}+6x=5+3$$

Add 5 and 3 to get 8.

$$-x^{2}+6x=8$$

Divide both sides by -1.

$$\frac{-x^{2}+6x}{-1}=\frac{8}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$x^{2}+\frac{6}{-1}x=\frac{8}{-1}$$

Divide 6 by -1.

$$x^{2}-6x=\frac{8}{-1}$$

Divide 8 by -1.

$$x^{2}-6x=-8$$

Divide -6, the coefficient of the x term, by 2 to get -3. Then add the square of -3 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-6x+\left(-3\right)^{2}=-8+\left(-3\right)^{2}$$

Square -3.

$$x^{2}-6x+9=-8+9$$

Add -8 to 9.

$$x^{2}-6x+9=1$$

Factor x^{2}-6x+9. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-3\right)^{2}=1$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-3\right)^{2}}=\sqrt{1}$$

Simplify.

$$x-3=1 x-3=-1$$

Add 3 to both sides of the equation.

$$x=4 x=2$$