3c^2+(4c-10c^2)+(5c-1)=1

Solution for 3c^2+(4c-10c^2)+(5c-1)=1 equation:

Simplifying
3c2 + (4c + -10c2) + (5c + -1) = 1

Remove parenthesis around (4c + -10c2)
3c2 + 4c + -10c2 + (5c + -1) = 1

Reorder the terms:
3c2 + 4c + -10c2 + (-1 + 5c) = 1

Remove parenthesis around (-1 + 5c)
3c2 + 4c + -10c2 + -1 + 5c = 1

Reorder the terms:
-1 + 4c + 5c + 3c2 + -10c2 = 1

Combine like terms: 4c + 5c = 9c
-1 + 9c + 3c2 + -10c2 = 1

Combine like terms: 3c2 + -10c2 = -7c2
-1 + 9c + -7c2 = 1

Solving
-1 + 9c + -7c2 = 1

Solving for variable 'c'.

Reorder the terms:
-1 + -1 + 9c + -7c2 = 1 + -1

Combine like terms: -1 + -1 = -2
-2 + 9c + -7c2 = 1 + -1

Combine like terms: 1 + -1 = 0
-2 + 9c + -7c2 = 0

Factor a trinomial.
(-1 + c)(2 + -7c) = 0

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

Simplifying
-1 + c = 0

Solving
-1 + c = 0

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

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

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

Combine like terms: 0 + 1 = 1
c = 1

Simplifying
c = 1
Subproblem 2
Set the factor '(2 + -7c)' equal to zero and attempt to solve:

Simplifying
2 + -7c = 0

Solving
2 + -7c = 0

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

Add '-2' to each side of the equation.
2 + -2 + -7c = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -7c = 0 + -2
-7c = 0 + -2

Combine like terms: 0 + -2 = -2
-7c = -2

Divide each side by '-7'.
c = 0.2857142857

Simplifying
c = 0.2857142857
Solution
c = {1, 0.2857142857}