9x-3-8x+4=6x^2-5x+1

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Solution for 9x-3-8x+4=6x^2-5x+1 equation: 


Simplifying
9x + -3 + -8x + 4 = 6x2 + -5x + 1

Reorder the terms:
-3 + 4 + 9x + -8x = 6x2 + -5x + 1

Combine like terms: -3 + 4 = 1
1 + 9x + -8x = 6x2 + -5x + 1

Combine like terms: 9x + -8x = 1x
1 + 1x = 6x2 + -5x + 1

Reorder the terms:
1 + 1x = 1 + -5x + 6x2

Add '-1' to each side of the equation.
1 + -1 + 1x = 1 + -5x + -1 + 6x2

Combine like terms: 1 + -1 = 0
0 + 1x = 1 + -5x + -1 + 6x2
1x = 1 + -5x + -1 + 6x2

Reorder the terms:
1x = 1 + -1 + -5x + 6x2

Combine like terms: 1 + -1 = 0
1x = 0 + -5x + 6x2
1x = -5x + 6x2

Solving
1x = -5x + 6x2

Solving for variable 'x'.

Combine like terms: 1x + 5x = 6x
6x + -6x2 = -5x + 6x2 + 5x + -6x2

Reorder the terms:
6x + -6x2 = -5x + 5x + 6x2 + -6x2

Combine like terms: -5x + 5x = 0
6x + -6x2 = 0 + 6x2 + -6x2
6x + -6x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
6x + -6x2 = 0

Factor out the Greatest Common Factor (GCF), '6x'.
6x(1 + -1x) = 0

Ignore the factor 6.

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 '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1
Solution
x = {0, 1}

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