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

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

Solve for x

$$x=-\frac{19}{20}=-0.95$$

Steps for Solving Linear Equation

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

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

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

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

Use the distributive property to multiply -3 by x^{2}+6x+9.

$$3x^{2}-2x-1-3x^{2}-18x-27=-9$$

Combine 3x^{2} and -3x^{2} to get 0.

$$-2x-1-18x-27=-9$$

Combine -2x and -18x to get -20x.

$$-20x-1-27=-9$$

Subtract 27 from -1 to get -28.

$$-20x-28=-9$$

Add 28 to both sides.

$$-20x=-9+28$$

Add -9 and 28 to get 19.

$$-20x=19$$

Divide both sides by -20.

$$x=\frac{19}{-20}$$

Fraction \frac{19}{-20} can be rewritten as -\frac{19}{20} by extracting the negative sign.

$$x=-\frac{19}{20}$$