Solve x(0,25x-3)-(0,5x+1)(0,5x-1)=0

$$x ( 0,25 x - 3 ) - ( 0,5 x + 1 ) ( 0,5 x - 1 ) = 0$$

Solve for x

$$x=\frac{1}{3}\approx 0,333333333$$

Steps for Solving Linear Equation

Use the distributive property to multiply x by 0,25x-3.

$$0,25x^{2}-3x-\left(0,5x+1\right)\left(0,5x-1\right)=0$$

Consider \left(0,5x+1\right)\left(0,5x-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.

$$0,25x^{2}-3x-\left(\left(0,5x\right)^{2}-1\right)=0$$

Expand \left(0,5x\right)^{2}.

$$0,25x^{2}-3x-\left(0,5^{2}x^{2}-1\right)=0$$

Calculate 0,5 to the power of 2 and get 0,25.

$$0,25x^{2}-3x-\left(0,25x^{2}-1\right)=0$$

To find the opposite of 0,25x^{2}-1, find the opposite of each term.

$$0,25x^{2}-3x-0,25x^{2}+1=0$$

Combine 0,25x^{2} and -0,25x^{2} to get 0.

$$-3x+1=0$$

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

$$-3x=-1$$

Divide both sides by -3.

$$x=\frac{-1}{-3}$$

Fraction \frac{-1}{-3} can be simplified to \frac{1}{3} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{1}{3}$$