0=4x^2+20x-200

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Solution for 0=4x^2+20x-200 equation: 


Simplifying
0 = 4x2 + 20x + -200

Reorder the terms:
0 = -200 + 20x + 4x2

Solving
0 = -200 + 20x + 4x2

Solving for variable 'x'.

Combine like terms: 0 + 200 = 200
200 + -20x + -4x2 = -200 + 20x + 4x2 + 200 + -20x + -4x2

Reorder the terms:
200 + -20x + -4x2 = -200 + 200 + 20x + -20x + 4x2 + -4x2

Combine like terms: -200 + 200 = 0
200 + -20x + -4x2 = 0 + 20x + -20x + 4x2 + -4x2
200 + -20x + -4x2 = 20x + -20x + 4x2 + -4x2

Combine like terms: 20x + -20x = 0
200 + -20x + -4x2 = 0 + 4x2 + -4x2
200 + -20x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
200 + -20x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(50 + -5x + -1x2) = 0

Factor a trinomial.
4((5 + -1x)(10 + x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5

Subproblem 2
Set the factor '(10 + x)' equal to zero and attempt to solve:

Simplifying
10 + x = 0

Solving
10 + x = 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 + x = 0 + -10

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

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

Simplifying
x = -10
Solution
x = {5, -10}

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