Solve (3x-2)^2=(x-5)(9x+1)

$$( 3 x - 2 ) ^ { 2 } = ( x - 5 ) ( 9 x + 1 )$$

Solve for x

$$x=-\frac{9}{32}=-0.28125$$

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}.

$$9x^{2}-12x+4=\left(x-5\right)\left(9x+1\right)$$

Use the distributive property to multiply x-5 by 9x+1 and combine like terms.

$$9x^{2}-12x+4=9x^{2}-44x-5$$

Subtract 9x^{2} from both sides.

$$9x^{2}-12x+4-9x^{2}=-44x-5$$

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

$$-12x+4=-44x-5$$

Add 44x to both sides.

$$-12x+4+44x=-5$$

Combine -12x and 44x to get 32x.

$$32x+4=-5$$

Subtract 4 from both sides.

$$32x=-5-4$$

Subtract 4 from -5 to get -9.

$$32x=-9$$

Divide both sides by 32.

$$x=\frac{-9}{32}$$

Fraction \frac{-9}{32} can be rewritten as -\frac{9}{32} by extracting the negative sign.

$$x=-\frac{9}{32}$$