Solve (x-3)^2-7x^2=-3(2x^2+3)

$$( x - 3 ) ^ { 2 } - 7 x ^ { 2 } = - 3 ( 2 x ^ { 2 } + 3 )$$

Solve for x

$$x=3$$

Steps for Solving Linear Equation

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

$$x^{2}-6x+9-7x^{2}=-3\left(2x^{2}+3\right)$$

Combine x^{2} and -7x^{2} to get -6x^{2}.

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

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

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

Add 6x^{2} to both sides.

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

Combine -6x^{2} and 6x^{2} to get 0.

$$-6x+9=-9$$

Subtract 9 from both sides.

$$-6x=-9-9$$

Subtract 9 from -9 to get -18.

$$-6x=-18$$

Divide both sides by -6.

$$x=\frac{-18}{-6}$$

Divide -18 by -6 to get 3.

$$x=3$$