Solve left(3x-2right)^2=(x-5)(9x+4)

$${ \left(3x-2 \right) }^{ 2 } =(x-5)(9x+4)$$

Solve for x

$$x=-\frac{24}{29}\approx -0.827586207$$

Steps for Solving Linear Equation

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

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

Use the distributive property to multiply x-5 by 9x+4 and combine like terms.

$$9x^{2}-12x+4=9x^{2}-41x-20$$

Subtract 9x^{2} from both sides.

$$9x^{2}-12x+4-9x^{2}=-41x-20$$

Combine 9x^{2} and -9x^{2} to get 0.

$$-12x+4=-41x-20$$

Add 41x to both sides.

$$-12x+4+41x=-20$$

Combine -12x and 41x to get 29x.

$$29x+4=-20$$

Subtract 4 from both sides.

$$29x=-20-4$$

Subtract 4 from -20 to get -24.

$$29x=-24$$

Divide both sides by 29.

$$x=\frac{-24}{29}$$

Fraction \frac{-24}{29} can be rewritten as -\frac{24}{29} by extracting the negative sign.

$$x=-\frac{24}{29}$$