Solve (3x-2)^3-(3x-2)(9x^2+6x+4)=6(1+3x)(1-3x)

$$( 3 x - 2 ) ^ { 3 } - ( 3 x - 2 ) ( 9 x ^ { 2 } + 6 x + 4 ) = 6 ( 1 + 3 x ) ( 1 - 3 x )$$

Solve for x

$$x=\frac{1}{6}\approx 0.166666667$$

Steps for Solving Linear Equation

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

$$27x^{3}-54x^{2}+36x-8-\left(3x-2\right)\left(9x^{2}+6x+4\right)=6\left(1+3x\right)\left(1-3x\right)$$

Use the distributive property to multiply 3x-2 by 9x^{2}+6x+4 and combine like terms.

$$27x^{3}-54x^{2}+36x-8-\left(27x^{3}-8\right)=6\left(1+3x\right)\left(1-3x\right)$$

To find the opposite of 27x^{3}-8, find the opposite of each term.

$$27x^{3}-54x^{2}+36x-8-27x^{3}+8=6\left(1+3x\right)\left(1-3x\right)$$

Combine 27x^{3} and -27x^{3} to get 0.

$$-54x^{2}+36x-8+8=6\left(1+3x\right)\left(1-3x\right)$$

Add -8 and 8 to get 0.

$$-54x^{2}+36x=6\left(1+3x\right)\left(1-3x\right)$$

Use the distributive property to multiply 6 by 1+3x.

$$-54x^{2}+36x=\left(6+18x\right)\left(1-3x\right)$$

Use the distributive property to multiply 6+18x by 1-3x and combine like terms.

$$-54x^{2}+36x=6-54x^{2}$$

Add 54x^{2} to both sides.

$$-54x^{2}+36x+54x^{2}=6$$

Combine -54x^{2} and 54x^{2} to get 0.

$$36x=6$$

Divide both sides by 36.

$$x=\frac{6}{36}$$

Reduce the fraction \frac{6}{36} to lowest terms by extracting and canceling out 6.

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