x(x)=2x^2-80x+1600

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Solution for x(x)=2x^2-80x+1600 equation: 


Simplifying
x(x) = 2x2 + -80x + 1600

Multiply x * x
x2 = 2x2 + -80x + 1600

Reorder the terms:
x2 = 1600 + -80x + 2x2

Solving
x2 = 1600 + -80x + 2x2

Solving for variable 'x'.

Reorder the terms:
-1600 + 80x + x2 + -2x2 = 1600 + -80x + 2x2 + -1600 + 80x + -2x2

Combine like terms: x2 + -2x2 = -1x2
-1600 + 80x + -1x2 = 1600 + -80x + 2x2 + -1600 + 80x + -2x2

Reorder the terms:
-1600 + 80x + -1x2 = 1600 + -1600 + -80x + 80x + 2x2 + -2x2

Combine like terms: 1600 + -1600 = 0
-1600 + 80x + -1x2 = 0 + -80x + 80x + 2x2 + -2x2
-1600 + 80x + -1x2 = -80x + 80x + 2x2 + -2x2

Combine like terms: -80x + 80x = 0
-1600 + 80x + -1x2 = 0 + 2x2 + -2x2
-1600 + 80x + -1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-1600 + 80x + -1x2 = 0

Factor a trinomial.
(-40 + x)(40 + -1x) = 0


Subproblem 1
Set the factor '(-40 + x)' equal to zero and attempt to solve:

Simplifying
-40 + x = 0

Solving
-40 + x = 0

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

Add '40' to each side of the equation.
-40 + 40 + x = 0 + 40

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

Combine like terms: 0 + 40 = 40
x = 40

Simplifying
x = 40

Subproblem 2
Set the factor '(40 + -1x)' equal to zero and attempt to solve:

Simplifying
40 + -1x = 0

Solving
40 + -1x = 0

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

Add '-40' to each side of the equation.
40 + -40 + -1x = 0 + -40

Combine like terms: 40 + -40 = 0
0 + -1x = 0 + -40
-1x = 0 + -40

Combine like terms: 0 + -40 = -40
-1x = -40

Divide each side by '-1'.
x = 40

Simplifying
x = 40
Solution
x = {40, 40}

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