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

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

Solve for x

$$x = -\frac{7}{3} = -2\frac{1}{3} \approx -2.333333333$$

Steps for Solving Linear Equation

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(3x+1\right)^{2}.

$$9x^{2}+6x+1=3\left(3x^{2}+x-2\right)$$

Use the distributive property to multiply 3 by 3x^{2}+x-2.

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

Subtract 9x^{2} from both sides.

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

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

$$6x+1=3x-6$$

Subtract 3x from both sides.

$$6x+1-3x=-6$$

Combine 6x and -3x to get 3x.

$$3x+1=-6$$

Subtract 1 from both sides.

$$3x=-6-1$$

Subtract 1 from -6 to get -7.

$$3x=-7$$

Divide both sides by 3.

$$x=\frac{-7}{3}$$

Fraction \frac{-7}{3} can be rewritten as -\frac{7}{3} by extracting the negative sign.

$$x=-\frac{7}{3}$$