10x+20x^2=100x^2-20x-3x

Solution for 10x+20x^2=100x^2-20x-3x equation:

Simplifying
10x + 20x2 = 100x2 + -20x + -3x

Reorder the terms:
10x + 20x2 = -20x + -3x + 100x2

Combine like terms: -20x + -3x = -23x
10x + 20x2 = -23x + 100x2

Solving
10x + 20x2 = -23x + 100x2

Solving for variable 'x'.

Reorder the terms:
10x + 23x + 20x2 + -100x2 = -23x + 100x2 + 23x + -100x2

Combine like terms: 10x + 23x = 33x
33x + 20x2 + -100x2 = -23x + 100x2 + 23x + -100x2

Combine like terms: 20x2 + -100x2 = -80x2
33x + -80x2 = -23x + 100x2 + 23x + -100x2

Reorder the terms:
33x + -80x2 = -23x + 23x + 100x2 + -100x2

Combine like terms: -23x + 23x = 0
33x + -80x2 = 0 + 100x2 + -100x2
33x + -80x2 = 100x2 + -100x2

Combine like terms: 100x2 + -100x2 = 0
33x + -80x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(33 + -80x) = 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 '(33 + -80x)' equal to zero and attempt to solve:

Simplifying
33 + -80x = 0

Solving
33 + -80x = 0

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

Add '-33' to each side of the equation.
33 + -33 + -80x = 0 + -33

Combine like terms: 33 + -33 = 0
0 + -80x = 0 + -33
-80x = 0 + -33

Combine like terms: 0 + -33 = -33
-80x = -33

Divide each side by '-80'.
x = 0.4125

Simplifying
x = 0.4125
Solution
x = {0, 0.4125}