10x^2-18x+20x=ax^2+bx

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Solution for 10x^2-18x+20x=ax^2+bx equation: 


Simplifying
10x2 + -18x + 20x = ax2 + bx

Reorder the terms:
-18x + 20x + 10x2 = ax2 + bx

Combine like terms: -18x + 20x = 2x
2x + 10x2 = ax2 + bx

Solving
2x + 10x2 = ax2 + bx

Solving for variable 'x'.

Reorder the terms:
-1ax2 + -1bx + 2x + 10x2 = ax2 + bx + -1ax2 + -1bx

Reorder the terms:
-1ax2 + -1bx + 2x + 10x2 = ax2 + -1ax2 + bx + -1bx

Combine like terms: ax2 + -1ax2 = 0
-1ax2 + -1bx + 2x + 10x2 = 0 + bx + -1bx
-1ax2 + -1bx + 2x + 10x2 = bx + -1bx

Combine like terms: bx + -1bx = 0
-1ax2 + -1bx + 2x + 10x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-1ax + -1b + 2 + 10x) = 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 '(-1ax + -1b + 2 + 10x)' equal to zero and attempt to solve:

Simplifying
-1ax + -1b + 2 + 10x = 0

Reorder the terms:
2 + -1ax + -1b + 10x = 0

Solving
2 + -1ax + -1b + 10x = 0

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

Add '-2' to each side of the equation.
2 + -1ax + -1b + -2 + 10x = 0 + -2

Reorder the terms:
2 + -2 + -1ax + -1b + 10x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1ax + -1b + 10x = 0 + -2
-1ax + -1b + 10x = 0 + -2

Combine like terms: 0 + -2 = -2
-1ax + -1b + 10x = -2

Add 'b' to each side of the equation.
-1ax + -1b + b + 10x = -2 + b

Combine like terms: -1b + b = 0
-1ax + 0 + 10x = -2 + b
-1ax + 10x = -2 + b

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {0}

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