Solve (3x(1+12x)-(6x-1)(6x+1)=2,5x

$$( 3 x ( 1 + 12 x ) - ( 6 x - 1 ) ( 6 x + 1 ) = 2,5 x$$

Solve for x

$$x=-2$$

Steps for Solving Linear Equation

Use the distributive property to multiply 3x by 1+12x.

$$3x+36x^{2}-\left(6x-1\right)\left(6x+1\right)=2,5x$$

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.

$$3x+36x^{2}-\left(\left(6x\right)^{2}-1\right)=2,5x$$

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

$$3x+36x^{2}-\left(6^{2}x^{2}-1\right)=2,5x$$

Calculate 6 to the power of 2 and get 36.

$$3x+36x^{2}-\left(36x^{2}-1\right)=2,5x$$

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

$$3x+36x^{2}-36x^{2}+1=2,5x$$

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

$$3x+1=2,5x$$

Subtract 2,5x from both sides.

$$3x+1-2,5x=0$$

Combine 3x and -2,5x to get 0,5x.

$$0,5x+1=0$$

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

$$0,5x=-1$$

Divide both sides by 0,5.

$$x=\frac{-1}{0,5}$$

Expand \frac{-1}{0,5} by multiplying both numerator and the denominator by 10.

$$x=\frac{-10}{5}$$

Divide -10 by 5 to get -2.

$$x=-2$$