x^2=100-80*x+16x^2

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Solution for x^2=100-80*x+16x^2 equation: 


Simplifying
x2 = 100 + -80x + 16x2

Solving
x2 = 100 + -80x + 16x2

Solving for variable 'x'.

Reorder the terms:
-100 + 80x + x2 + -16x2 = 100 + -80x + 16x2 + -100 + 80x + -16x2

Combine like terms: x2 + -16x2 = -15x2
-100 + 80x + -15x2 = 100 + -80x + 16x2 + -100 + 80x + -16x2

Reorder the terms:
-100 + 80x + -15x2 = 100 + -100 + -80x + 80x + 16x2 + -16x2

Combine like terms: 100 + -100 = 0
-100 + 80x + -15x2 = 0 + -80x + 80x + 16x2 + -16x2
-100 + 80x + -15x2 = -80x + 80x + 16x2 + -16x2

Combine like terms: -80x + 80x = 0
-100 + 80x + -15x2 = 0 + 16x2 + -16x2
-100 + 80x + -15x2 = 16x2 + -16x2

Combine like terms: 16x2 + -16x2 = 0
-100 + 80x + -15x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-20 + 16x + -3x2) = 0

Factor a trinomial.
5((-10 + 3x)(2 + -1x)) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-10 + 3x)' equal to zero and attempt to solve:

Simplifying
-10 + 3x = 0

Solving
-10 + 3x = 0

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

Add '10' to each side of the equation.
-10 + 10 + 3x = 0 + 10

Combine like terms: -10 + 10 = 0
0 + 3x = 0 + 10
3x = 0 + 10

Combine like terms: 0 + 10 = 10
3x = 10

Divide each side by '3'.
x = 3.333333333

Simplifying
x = 3.333333333

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {3.333333333, 2}

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