Solve (2-3x)(3x+2)/5+(3x-2)^2/5=2x-5x+2/4

$$\frac { ( 2 - 3 x ) ( 3 x + 2 ) } { 5 } + \frac { ( 3 x - 2 ) ^ { 2 } } { 5 } = 2 x - \frac { 5 x + 2 } { 4 }$$

Solve for x

$$x=\frac{2}{3}\approx 0.666666667$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 20, the least common multiple of 5,4.

$$4\left(2-3x\right)\left(3x+2\right)+4\left(3x-2\right)^{2}=40x-5\left(5x+2\right)$$

Use the distributive property to multiply 4 by 2-3x.

$$\left(8-12x\right)\left(3x+2\right)+4\left(3x-2\right)^{2}=40x-5\left(5x+2\right)$$

Use the distributive property to multiply 8-12x by 3x+2 and combine like terms.

$$16-36x^{2}+4\left(3x-2\right)^{2}=40x-5\left(5x+2\right)$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(3x-2\right)^{2}.

$$16-36x^{2}+4\left(9x^{2}-12x+4\right)=40x-5\left(5x+2\right)$$

Use the distributive property to multiply 4 by 9x^{2}-12x+4.

$$16-36x^{2}+36x^{2}-48x+16=40x-5\left(5x+2\right)$$

Combine -36x^{2} and 36x^{2} to get 0.

$$16-48x+16=40x-5\left(5x+2\right)$$

Add 16 and 16 to get 32.

$$32-48x=40x-5\left(5x+2\right)$$

Use the distributive property to multiply -5 by 5x+2.

$$32-48x=40x-25x-10$$

Combine 40x and -25x to get 15x.

$$32-48x=15x-10$$

Subtract 15x from both sides.

$$32-48x-15x=-10$$

Combine -48x and -15x to get -63x.

$$32-63x=-10$$

Subtract 32 from both sides.

$$-63x=-10-32$$

Subtract 32 from -10 to get -42.

$$-63x=-42$$

Divide both sides by -63.

$$x=\frac{-42}{-63}$$

Reduce the fraction \frac{-42}{-63} to lowest terms by extracting and canceling out -21.

$$x=\frac{2}{3}$$