Hx=fx+gx

Simple and best practice solution for Hx=fx+gx equation. Check how easy it is, and learn it for the future. Our solution is simple, and easy to understand, so don`t hesitate to use it as a solution of your homework.

If it's not what You are looking for type in the equation solver your own equation and let us solve it.

Solution for Hx=fx+gx equation: 


Simplifying
Hx = fx + gx

Solving
xH = fx + gx

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-1fx' to each side of the equation.
-1fx + xH = fx + -1fx + gx

Combine like terms: fx + -1fx = 0
-1fx + xH = 0 + gx
-1fx + xH = gx

Add '-1gx' to each side of the equation.
-1fx + -1gx + xH = gx + -1gx

Combine like terms: gx + -1gx = 0
-1fx + -1gx + xH = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-1f + -1g + H) = 0


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

Move all terms containing x to the left, all other terms to the right.

Simplifying
x = 0

Subproblem 2
Set the factor '(-1f + -1g + H)' equal to zero and attempt to solve:

Simplifying
-1f + -1g + H = 0

Reorder the terms:
H + -1f + -1g = 0

Solving
H + -1f + -1g = 0

Move all terms containing x to the left, all other terms to the right.

Add '-1H' to each side of the equation.
H + -1f + -1H + -1g = 0 + -1H

Reorder the terms:
H + -1H + -1f + -1g = 0 + -1H

Combine like terms: H + -1H = 0
0 + -1f + -1g = 0 + -1H
-1f + -1g = 0 + -1H
Remove the zero:
-1f + -1g = -1H

Add 'f' to each side of the equation.
-1f + f + -1g = -1H + f

Combine like terms: -1f + f = 0
0 + -1g = -1H + f
-1g = -1H + f

Add 'g' to each side of the equation.
-1g + g = -1H + f + g

Combine like terms: -1g + g = 0
0 = -1H + f + g

Simplifying
0 = -1H + f + g

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {0}

See similar equations:

| x^4-4x^3+6x^2-4x+1=16 | | -3(2x-4)+5-(4x+2)= | | b=4/3(j-4) | | 5x-2x=43+20 | | .5-x+3.5=x-2 | | b=b^2+7b-27 | | 5(x-3)+4+3x= | | 4y/9=40 | | x^2+4x=8x-7 | | 3c+5c+8c-4= | | 8x+5=2x+9 | | 9+4x-12=12 | | -3x^2+7X^2= | | 80=10(v+8) | | 23x+5=-16x+35 | | 4a+1.5a=0 | | 6n=5n+31 | | 7t+28=-42 | | X/12=6/7 | | 6r-1=3 | | 5r^2-1=0 | | x+28=4x-4 | | x+3=4(2x-6) | | s/2-9=1 | | 2u+5u=7 | | -3(-2x+9)= | | R+4+2r=-21 | | 0.2(1-d)=2(4+0.1d) | | 4b^2-b-8=0 | | p/4=16. | | 115+24+x=180 | | z^2-iz-3z+a+2i=0 |

Equations solver categories