Solve 2(2x+3)-3/2x(x+1)=x(2x+3)-7/2x^2

$$2 ( 2 x + 3 ) - \frac { 3 } { 2 } x ( x + 1 ) = x ( 2 x + 3 ) - \frac { 7 } { 2 } x ^ { 2 }$$

Solve for x

$$x=12$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2 by 2x+3.

$$4x+6-\frac{3}{2}x\left(x+1\right)=x\left(2x+3\right)-\frac{7}{2}x^{2}$$

Use the distributive property to multiply x by 2x+3.

$$4x+6-\frac{3}{2}x\left(x+1\right)=2x^{2}+3x-\frac{7}{2}x^{2}$$

Combine 2x^{2} and -\frac{7}{2}x^{2} to get -\frac{3}{2}x^{2}.

$$4x+6-\frac{3}{2}x\left(x+1\right)=-\frac{3}{2}x^{2}+3x$$

Add \frac{3}{2}x^{2} to both sides.

$$4x+6-\frac{3}{2}x\left(x+1\right)+\frac{3}{2}x^{2}=3x$$

Subtract 3x from both sides.

$$4x+6-\frac{3}{2}x\left(x+1\right)+\frac{3}{2}x^{2}-3x=0$$

Use the distributive property to multiply -\frac{3}{2}x by x+1.

$$4x+6-\frac{3}{2}x^{2}-\frac{3}{2}x+\frac{3}{2}x^{2}-3x=0$$

Combine 4x and -\frac{3}{2}x to get \frac{5}{2}x.

$$\frac{5}{2}x+6-\frac{3}{2}x^{2}+\frac{3}{2}x^{2}-3x=0$$

Combine -\frac{3}{2}x^{2} and \frac{3}{2}x^{2} to get 0.

$$\frac{5}{2}x+6-3x=0$$

Combine \frac{5}{2}x and -3x to get -\frac{1}{2}x.

$$-\frac{1}{2}x+6=0$$

Subtract 6 from both sides. Anything subtracted from zero gives its negation.

$$-\frac{1}{2}x=-6$$

Multiply both sides by -2, the reciprocal of -\frac{1}{2}.

$$x=-6\left(-2\right)$$

Multiply -6 and -2 to get 12.

$$x=12$$