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

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

Solve for x

$$x=-\frac{5}{33}\approx -0.151515152$$

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}.

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

Add 1 and 4 to get 5.

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

Use the distributive property to multiply x-5 by 9.

$$5+9x^{2}-12x=\left(9x-45\right)x$$

Use the distributive property to multiply 9x-45 by x.

$$5+9x^{2}-12x=9x^{2}-45x$$

Subtract 9x^{2} from both sides.

$$5+9x^{2}-12x-9x^{2}=-45x$$

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

$$5-12x=-45x$$

Add 45x to both sides.

$$5-12x+45x=0$$

Combine -12x and 45x to get 33x.

$$5+33x=0$$

Subtract 5 from both sides. Anything subtracted from zero gives its negation.

$$33x=-5$$

Divide both sides by 33.

$$x=\frac{-5}{33}$$

Fraction \frac{-5}{33} can be rewritten as -\frac{5}{33} by extracting the negative sign.

$$x=-\frac{5}{33}$$