2*x(x-1)=3*x*x+1

Solution for 2*x(x-1)=3*x*x+1 equation:

Simplifying
2x(x + -1) = 3x * x + 1

Reorder the terms:
2x(-1 + x) = 3x * x + 1
(-1 * 2x + x * 2x) = 3x * x + 1
(-2x + 2x2) = 3x * x + 1

Multiply x * x
-2x + 2x2 = 3x2 + 1

Reorder the terms:
-2x + 2x2 = 1 + 3x2

Solving
-2x + 2x2 = 1 + 3x2

Solving for variable 'x'.

Reorder the terms:
-1 + -2x + 2x2 + -3x2 = 1 + 3x2 + -1 + -3x2

Combine like terms: 2x2 + -3x2 = -1x2
-1 + -2x + -1x2 = 1 + 3x2 + -1 + -3x2

Reorder the terms:
-1 + -2x + -1x2 = 1 + -1 + 3x2 + -3x2

Combine like terms: 1 + -1 = 0
-1 + -2x + -1x2 = 0 + 3x2 + -3x2
-1 + -2x + -1x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-1 + -2x + -1x2 = 0

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

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

Ignore the factor -1.
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 + 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
Solution
x = {-1, -1}