Solve (5x-2)(x+3)=13(x-3)

$$( 5 x - 2 ) ( x + 3 ) = 13 ( x - 3 )$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{165}i}{5}\approx -0-2.569046516i$$

$$x=\frac{\sqrt{165}i}{5}\approx 2.569046516i$$

Steps by Finding Square Root

Use the distributive property to multiply 5x-2 by x+3 and combine like terms.

$$5x^{2}+13x-6=13\left(x-3\right)$$

Use the distributive property to multiply 13 by x-3.

$$5x^{2}+13x-6=13x-39$$

Subtract 13x from both sides.

$$5x^{2}+13x-6-13x=-39$$

Combine 13x and -13x to get 0.

$$5x^{2}-6=-39$$

Add 6 to both sides.

$$5x^{2}=-39+6$$

Add -39 and 6 to get -33.

$$5x^{2}=-33$$

Divide both sides by 5.

$$x^{2}=-\frac{33}{5}$$

The equation is now solved.

$$x=\frac{\sqrt{165}i}{5} x=-\frac{\sqrt{165}i}{5}$$

Steps Using the Quadratic Formula

Use the distributive property to multiply 5x-2 by x+3 and combine like terms.

$$5x^{2}+13x-6=13\left(x-3\right)$$

Use the distributive property to multiply 13 by x-3.

$$5x^{2}+13x-6=13x-39$$

Subtract 13x from both sides.

$$5x^{2}+13x-6-13x=-39$$

Combine 13x and -13x to get 0.

$$5x^{2}-6=-39$$

Add 39 to both sides.

$$5x^{2}-6+39=0$$

Add -6 and 39 to get 33.

$$5x^{2}+33=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 5 for a, 0 for b, and 33 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 5\times 33}}{2\times 5}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 5\times 33}}{2\times 5}$$

Multiply -4 times 5.

$$x=\frac{0±\sqrt{-20\times 33}}{2\times 5}$$

Multiply -20 times 33.

$$x=\frac{0±\sqrt{-660}}{2\times 5}$$

Take the square root of -660.

$$x=\frac{0±2\sqrt{165}i}{2\times 5}$$

Multiply 2 times 5.

$$x=\frac{0±2\sqrt{165}i}{10}$$

Now solve the equation x=\frac{0±2\sqrt{165}i}{10} when ± is plus.

$$x=\frac{\sqrt{165}i}{5}$$

Now solve the equation x=\frac{0±2\sqrt{165}i}{10} when ± is minus.

$$x=-\frac{\sqrt{165}i}{5}$$

The equation is now solved.

$$x=\frac{\sqrt{165}i}{5} x=-\frac{\sqrt{165}i}{5}$$