How to solve an equation?

Give a example and solve and please write the steps also.

Solve--2x^2=-4

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                     -2*x^2-(-4)=0 

Step by step solution :

STEP1:Equation at the end of step 1

STEP2:

STEP3:Pulling out like terms

 3.1     Pull out like factors :

   4 - 2x²  =   -2 • (x² - 2) 

Trying to factor as a Difference of Squares:

 3.2      Factoring:  x² - 2 

Theory : A difference of two perfect squares,  A² - B²  can be factored into  (A+B) • (A-B)

Proof :  (A+B) • (A-B) =
         A² - AB + BA - B² =
         A² - AB + AB - B² =
         A² - B²

Note :  AB = BA is the commutative property of multiplication.

Note :  - AB + AB equals zero and is therefore eliminated from the expression.

Check : 2 is not a square !!

Ruling : Binomial can not be factored as the difference of two perfect squares.

Equation at the end of step3:

STEP4:

Equations which are never true:

 4.1      Solve :    -2   =  0

This equation has no solution.
A a non-zero constant never equals zero.

Solving a Single Variable Equation:

 4.2      Solve  :    x²-2 = 0 

 Add  2  to both sides of the equation : 
                      x² = 2
 
 When two things are equal, their square roots are equal. Taking the square root of the two sides of the equation we get:  
                      x  =  ± √ 2  

 The equation has two real solutions  
 These solutions are  x = ± √2 = ± 1.4142