Solve (-3x+1)(x-4)=x-4

$$(-3x+1)(x-4)=x-4$$

Solve for x

$$x=4$$

$$x=0$$

Steps Using the Quadratic Formula

Use the distributive property to multiply -3x+1 by x-4 and combine like terms.

$$-3x^{2}+13x-4=x-4$$

Subtract x from both sides.

$$-3x^{2}+13x-4-x=-4$$

Combine 13x and -x to get 12x.

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

Add 4 to both sides.

$$-3x^{2}+12x-4+4=0$$

Add -4 and 4 to get 0.

$$-3x^{2}+12x=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -3 for a, 12 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-12±\sqrt{12^{2}}}{2\left(-3\right)}$$

Take the square root of 12^{2}.

$$x=\frac{-12±12}{2\left(-3\right)}$$

Multiply 2 times -3.

$$x=\frac{-12±12}{-6}$$

Now solve the equation x=\frac{-12±12}{-6} when ± is plus. Add -12 to 12.

$$x=\frac{0}{-6}$$

Divide 0 by -6.

$$x=0$$

Now solve the equation x=\frac{-12±12}{-6} when ± is minus. Subtract 12 from -12.

$$x=-\frac{24}{-6}$$

Divide -24 by -6.

$$x=4$$

The equation is now solved.

$$x=0 x=4$$

Steps for Completing the Square

Use the distributive property to multiply -3x+1 by x-4 and combine like terms.

$$-3x^{2}+13x-4=x-4$$

Subtract x from both sides.

$$-3x^{2}+13x-4-x=-4$$

Combine 13x and -x to get 12x.

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

Add 4 to both sides.

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

Add -4 and 4 to get 0.

$$-3x^{2}+12x=0$$

Divide both sides by -3.

$$\frac{-3x^{2}+12x}{-3}=\frac{0}{-3}$$

Dividing by -3 undoes the multiplication by -3.

$$x^{2}+\frac{12}{-3}x=\frac{0}{-3}$$

Divide 12 by -3.

$$x^{2}-4x=\frac{0}{-3}$$

Divide 0 by -3.

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

Divide -4, the coefficient of the x term, by 2 to get -2. Then add the square of -2 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-4x+\left(-2\right)^{2}=\left(-2\right)^{2}$$

Square -2.

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

Factor x^{2}-4x+4. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-2\right)^{2}=4$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-2\right)^{2}}=\sqrt{4}$$

Simplify.

$$x-2=2 x-2=-2$$

Add 2 to both sides of the equation.

$$x=4 x=0$$