-2x^2+x+1=mx+1

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Solution for -2x^2+x+1=mx+1 equation:


Simplifying
-2x2 + x + 1 = mx + 1

Reorder the terms:
1 + x + -2x2 = mx + 1

Reorder the terms:
1 + x + -2x2 = 1 + mx

Add '-1' to each side of the equation.
1 + x + -1 + -2x2 = 1 + -1 + mx

Reorder the terms:
1 + -1 + x + -2x2 = 1 + -1 + mx

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

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

Solving
x + -2x2 = mx

Solving for variable 'x'.

Reorder the terms:
-1mx + x + -2x2 = mx + -1mx

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

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

Simplifying
-1m + 1 + -2x = 0

Reorder the terms:
1 + -1m + -2x = 0

Solving
1 + -1m + -2x = 0

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

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

Reorder the terms:
1 + -1 + -1m + -2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1m + -2x = 0 + -1
-1m + -2x = 0 + -1

Combine like terms: 0 + -1 = -1
-1m + -2x = -1

Add 'm' to each side of the equation.
-1m + m + -2x = -1 + m

Combine like terms: -1m + m = 0
0 + -2x = -1 + m
-2x = -1 + m

Divide each side by '-2'.
x = 0.5 + -0.5m

Simplifying
x = 0.5 + -0.5m
Solution
x = {0, 0.5 + -0.5m}

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