Solve 3x(4+12x)-(6x-1)(6x+1)=11x

$$3 x ( 4 + 12 x ) - ( 6 x - 1 ) ( 6 x + 1 ) = 11 x$$

Solve for x

$$x=-1$$

Steps for Solving Linear Equation

Use the distributive property to multiply 3x by 4+12x.

$$12x+36x^{2}-\left(6x-1\right)\left(6x+1\right)=11x$$

Consider \left(6x-1\right)\left(6x+1\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.

$$12x+36x^{2}-\left(\left(6x\right)^{2}-1\right)=11x$$

Expand \left(6x\right)^{2}.

$$12x+36x^{2}-\left(6^{2}x^{2}-1\right)=11x$$

Calculate 6 to the power of 2 and get 36.

$$12x+36x^{2}-\left(36x^{2}-1\right)=11x$$

To find the opposite of 36x^{2}-1, find the opposite of each term.

$$12x+36x^{2}-36x^{2}+1=11x$$

Combine 36x^{2} and -36x^{2} to get 0.

$$12x+1=11x$$

Subtract 11x from both sides.

$$12x+1-11x=0$$

Combine 12x and -11x to get x.

$$x+1=0$$

Subtract 1 from both sides. Anything subtracted from zero gives its negation.

$$x=-1$$