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

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

Solve for x

$$x=4$$

Steps for Solving Linear Equation

Consider \left(1-3x\right)\left(1+3x\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 1.

$$1-\left(3x\right)^{2}-2\left(x-5\right)=3-9x^{2}$$

Expand \left(3x\right)^{2}.

$$1-3^{2}x^{2}-2\left(x-5\right)=3-9x^{2}$$

Calculate 3 to the power of 2 and get 9.

$$1-9x^{2}-2\left(x-5\right)=3-9x^{2}$$

Use the distributive property to multiply -2 by x-5.

$$1-9x^{2}-2x+10=3-9x^{2}$$

Add 1 and 10 to get 11.

$$11-9x^{2}-2x=3-9x^{2}$$

Add 9x^{2} to both sides.

$$11-9x^{2}-2x+9x^{2}=3$$

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

$$11-2x=3$$

Subtract 11 from both sides.

$$-2x=3-11$$

Subtract 11 from 3 to get -8.

$$-2x=-8$$

Divide both sides by -2.

$$x=\frac{-8}{-2}$$

Divide -8 by -2 to get 4.

$$x=4$$