100=x^2+4x^2-40x+100

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Solution for 100=x^2+4x^2-40x+100 equation: 


Simplifying
100 = x2 + 4x2 + -40x + 100

Reorder the terms:
100 = 100 + -40x + x2 + 4x2

Combine like terms: x2 + 4x2 = 5x2
100 = 100 + -40x + 5x2

Add '-100' to each side of the equation.
100 + -100 = 100 + -40x + -100 + 5x2

Combine like terms: 100 + -100 = 0
0 = 100 + -40x + -100 + 5x2

Reorder the terms:
0 = 100 + -100 + -40x + 5x2

Combine like terms: 100 + -100 = 0
0 = 0 + -40x + 5x2
0 = -40x + 5x2

Solving
0 = -40x + 5x2

Solving for variable 'x'.
Remove the zero:
40x + -5x2 = -40x + 5x2 + 40x + -5x2

Reorder the terms:
40x + -5x2 = -40x + 40x + 5x2 + -5x2

Combine like terms: -40x + 40x = 0
40x + -5x2 = 0 + 5x2 + -5x2
40x + -5x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
40x + -5x2 = 0

Factor out the Greatest Common Factor (GCF), '5x'.
5x(8 + -1x) = 0

Ignore the factor 5.

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 '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {0, 8}

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