Solve (-x-5)(-x+5)+(-2x+4)^2=(5x-1)(x+2)

$$( - x - 5 ) ( - x + 5 ) + ( - 2 x + 4 ) ^ { 2 } = ( 5 x - 1 ) ( x + 2 )$$

Solve for x

$$x=-\frac{7}{25}=-0.28$$

Steps for Solving Linear Equation

Consider \left(-x-5\right)\left(-x+5\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 5.

$$\left(-x\right)^{2}-25+\left(-2x+4\right)^{2}=\left(5x-1\right)\left(x+2\right)$$

Calculate -x to the power of 2 and get x^{2}.

$$x^{2}-25+\left(-2x+4\right)^{2}=\left(5x-1\right)\left(x+2\right)$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(-2x+4\right)^{2}.

$$x^{2}-25+4x^{2}-16x+16=\left(5x-1\right)\left(x+2\right)$$

Combine x^{2} and 4x^{2} to get 5x^{2}.

$$5x^{2}-25-16x+16=\left(5x-1\right)\left(x+2\right)$$

Add -25 and 16 to get -9.

$$5x^{2}-9-16x=\left(5x-1\right)\left(x+2\right)$$

Use the distributive property to multiply 5x-1 by x+2 and combine like terms.

$$5x^{2}-9-16x=5x^{2}+9x-2$$

Subtract 5x^{2} from both sides.

$$5x^{2}-9-16x-5x^{2}=9x-2$$

Combine 5x^{2} and -5x^{2} to get 0.

$$-9-16x=9x-2$$

Subtract 9x from both sides.

$$-9-16x-9x=-2$$

Combine -16x and -9x to get -25x.

$$-9-25x=-2$$

Add 9 to both sides.

$$-25x=-2+9$$

Add -2 and 9 to get 7.

$$-25x=7$$

Divide both sides by -25.

$$x=\frac{7}{-25}$$

Fraction \frac{7}{-25} can be rewritten as -\frac{7}{25} by extracting the negative sign.

$$x=-\frac{7}{25}$$