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

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

Solve for x

$$x=2$$

$$x=0$$

Steps Using the Quadratic Formula

Use the distributive property to multiply 2x-1 by 3x-2 and combine like terms.

$$6x^{2}-7x+2=5x+2$$

Subtract 5x from both sides.

$$6x^{2}-7x+2-5x=2$$

Combine -7x and -5x to get -12x.

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

Subtract 2 from both sides.

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

Subtract 2 from 2 to get 0.

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

This equation is in standard form: ax^{2}+bx+c=0. Substitute 6 for a, -12 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-12\right)±\sqrt{\left(-12\right)^{2}}}{2\times 6}$$

Take the square root of \left(-12\right)^{2}.

$$x=\frac{-\left(-12\right)±12}{2\times 6}$$

The opposite of -12 is 12.

$$x=\frac{12±12}{2\times 6}$$

Multiply 2 times 6.

$$x=\frac{12±12}{12}$$

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

$$x=\frac{24}{12}$$

Divide 24 by 12.

$$x=2$$

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

$$x=\frac{0}{12}$$

Divide 0 by 12.

$$x=0$$

The equation is now solved.

$$x=2 x=0$$

Steps for Completing the Square

Use the distributive property to multiply 2x-1 by 3x-2 and combine like terms.

$$6x^{2}-7x+2=5x+2$$

Subtract 5x from both sides.

$$6x^{2}-7x+2-5x=2$$

Combine -7x and -5x to get -12x.

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

Subtract 2 from both sides.

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

Subtract 2 from 2 to get 0.

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

Divide both sides by 6.

$$\frac{6x^{2}-12x}{6}=\frac{0}{6}$$

Dividing by 6 undoes the multiplication by 6.

$$x^{2}+\left(-\frac{12}{6}\right)x=\frac{0}{6}$$

Divide -12 by 6.

$$x^{2}-2x=\frac{0}{6}$$

Divide 0 by 6.

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

Divide -2, the coefficient of the x term, by 2 to get -1. Then add the square of -1 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

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

Factor x^{2}-2x+1. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

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

Take the square root of both sides of the equation.

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

Simplify.

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

Add 1 to both sides of the equation.

$$x=2 x=0$$