Solve 2x(x+1)=x(x+5)+3(12-x)

$$2 x ( x + 1 ) = x ( x + 5 ) + 3 ( 12 - x )$$

Solve for x

$$x=-6$$

$$x=6$$

Steps by Finding Square Root

Use the distributive property to multiply 2x by x+1.

$$2x^{2}+2x=x\left(x+5\right)+3\left(12-x\right)$$

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

$$2x^{2}+2x=x^{2}+5x+3\left(12-x\right)$$

Use the distributive property to multiply 3 by 12-x.

$$2x^{2}+2x=x^{2}+5x+36-3x$$

Combine 5x and -3x to get 2x.

$$2x^{2}+2x=x^{2}+2x+36$$

Subtract x^{2} from both sides.

$$2x^{2}+2x-x^{2}=2x+36$$

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

$$x^{2}+2x=2x+36$$

Subtract 2x from both sides.

$$x^{2}+2x-2x=36$$

Combine 2x and -2x to get 0.

$$x^{2}=36$$

Take the square root of both sides of the equation.

$$x=6 x=-6$$

Steps Using the Quadratic Formula

Use the distributive property to multiply 2x by x+1.

$$2x^{2}+2x=x\left(x+5\right)+3\left(12-x\right)$$

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

$$2x^{2}+2x=x^{2}+5x+3\left(12-x\right)$$

Use the distributive property to multiply 3 by 12-x.

$$2x^{2}+2x=x^{2}+5x+36-3x$$

Combine 5x and -3x to get 2x.

$$2x^{2}+2x=x^{2}+2x+36$$

Subtract x^{2} from both sides.

$$2x^{2}+2x-x^{2}=2x+36$$

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

$$x^{2}+2x=2x+36$$

Subtract 2x from both sides.

$$x^{2}+2x-2x=36$$

Combine 2x and -2x to get 0.

$$x^{2}=36$$

Subtract 36 from both sides.

$$x^{2}-36=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -36 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-36\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-36\right)}}{2}$$

Multiply -4 times -36.

$$x=\frac{0±\sqrt{144}}{2}$$

Take the square root of 144.

$$x=\frac{0±12}{2}$$

Now solve the equation x=\frac{0±12}{2} when ± is plus. Divide 12 by 2.

$$x=6$$

Now solve the equation x=\frac{0±12}{2} when ± is minus. Divide -12 by 2.

$$x=-6$$

The equation is now solved.

$$x=6 x=-6$$