3x-5x^2+1=6-7x

Solution for 3x-5x^2+1=6-7x equation:

Simplifying
3x + -5x2 + 1 = 6 + -7x

Reorder the terms:
1 + 3x + -5x2 = 6 + -7x

Solving
1 + 3x + -5x2 = 6 + -7x

Solving for variable 'x'.

Reorder the terms:
1 + -6 + 3x + 7x + -5x2 = 6 + -7x + -6 + 7x

Combine like terms: 1 + -6 = -5
-5 + 3x + 7x + -5x2 = 6 + -7x + -6 + 7x

Combine like terms: 3x + 7x = 10x
-5 + 10x + -5x2 = 6 + -7x + -6 + 7x

Reorder the terms:
-5 + 10x + -5x2 = 6 + -6 + -7x + 7x

Combine like terms: 6 + -6 = 0
-5 + 10x + -5x2 = 0 + -7x + 7x
-5 + 10x + -5x2 = -7x + 7x

Combine like terms: -7x + 7x = 0
-5 + 10x + -5x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-1 + 2x + -1x2) = 0

Factor a trinomial.
5((-1 + x)(1 + -1x)) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(-1 + x)' equal to zero and attempt to solve:

Simplifying
-1 + x = 0

Solving
-1 + x = 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 + x = 0 + 1

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

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

Simplifying
x = 1
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 = {1, 1}