Solve 5(x+3)(x-2)=(x+6)(x-1)

$$5(x+3)(x-2)=(x+6)(x-1)$$

Solve for x

$$x=\sqrt{6}\approx 2.449489743$$

$$x=-\sqrt{6}\approx -2.449489743$$

Steps by Finding Square Root

Use the distributive property to multiply 5 by x+3.

$$\left(5x+15\right)\left(x-2\right)=\left(x+6\right)\left(x-1\right)$$

Use the distributive property to multiply 5x+15 by x-2 and combine like terms.

$$5x^{2}+5x-30=\left(x+6\right)\left(x-1\right)$$

Use the distributive property to multiply x+6 by x-1 and combine like terms.

$$5x^{2}+5x-30=x^{2}+5x-6$$

Subtract x^{2} from both sides.

$$5x^{2}+5x-30-x^{2}=5x-6$$

Combine 5x^{2} and -x^{2} to get 4x^{2}.

$$4x^{2}+5x-30=5x-6$$

Subtract 5x from both sides.

$$4x^{2}+5x-30-5x=-6$$

Combine 5x and -5x to get 0.

$$4x^{2}-30=-6$$

Add 30 to both sides.

$$4x^{2}=-6+30$$

Add -6 and 30 to get 24.

$$4x^{2}=24$$

Divide both sides by 4.

$$x^{2}=\frac{24}{4}$$

Divide 24 by 4 to get 6.

$$x^{2}=6$$

Take the square root of both sides of the equation.

$$x=\sqrt{6} x=-\sqrt{6}$$

Steps Using the Quadratic Formula

Use the distributive property to multiply 5 by x+3.

$$\left(5x+15\right)\left(x-2\right)=\left(x+6\right)\left(x-1\right)$$

Use the distributive property to multiply 5x+15 by x-2 and combine like terms.

$$5x^{2}+5x-30=\left(x+6\right)\left(x-1\right)$$

Use the distributive property to multiply x+6 by x-1 and combine like terms.

$$5x^{2}+5x-30=x^{2}+5x-6$$

Subtract x^{2} from both sides.

$$5x^{2}+5x-30-x^{2}=5x-6$$

Combine 5x^{2} and -x^{2} to get 4x^{2}.

$$4x^{2}+5x-30=5x-6$$

Subtract 5x from both sides.

$$4x^{2}+5x-30-5x=-6$$

Combine 5x and -5x to get 0.

$$4x^{2}-30=-6$$

Add 6 to both sides.

$$4x^{2}-30+6=0$$

Add -30 and 6 to get -24.

$$4x^{2}-24=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 4 for a, 0 for b, and -24 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 4\left(-24\right)}}{2\times 4}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 4\left(-24\right)}}{2\times 4}$$

Multiply -4 times 4.

$$x=\frac{0±\sqrt{-16\left(-24\right)}}{2\times 4}$$

Multiply -16 times -24.

$$x=\frac{0±\sqrt{384}}{2\times 4}$$

Take the square root of 384.

$$x=\frac{0±8\sqrt{6}}{2\times 4}$$

Multiply 2 times 4.

$$x=\frac{0±8\sqrt{6}}{8}$$

Now solve the equation x=\frac{0±8\sqrt{6}}{8} when ± is plus.

$$x=\sqrt{6}$$

Now solve the equation x=\frac{0±8\sqrt{6}}{8} when ± is minus.

$$x=-\sqrt{6}$$

The equation is now solved.

$$x=\sqrt{6} x=-\sqrt{6}$$