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

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


Simplifying
3x2 + 2x = x2 + 5x + -1

Reorder the terms:
2x + 3x2 = x2 + 5x + -1

Reorder the terms:
2x + 3x2 = -1 + 5x + x2

Solving
2x + 3x2 = -1 + 5x + x2

Solving for variable 'x'.

Reorder the terms:
1 + 2x + -5x + 3x2 + -1x2 = -1 + 5x + x2 + 1 + -5x + -1x2

Combine like terms: 2x + -5x = -3x
1 + -3x + 3x2 + -1x2 = -1 + 5x + x2 + 1 + -5x + -1x2

Combine like terms: 3x2 + -1x2 = 2x2
1 + -3x + 2x2 = -1 + 5x + x2 + 1 + -5x + -1x2

Reorder the terms:
1 + -3x + 2x2 = -1 + 1 + 5x + -5x + x2 + -1x2

Combine like terms: -1 + 1 = 0
1 + -3x + 2x2 = 0 + 5x + -5x + x2 + -1x2
1 + -3x + 2x2 = 5x + -5x + x2 + -1x2

Combine like terms: 5x + -5x = 0
1 + -3x + 2x2 = 0 + x2 + -1x2
1 + -3x + 2x2 = x2 + -1x2

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

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


Subproblem 1
Set the factor '(1 + -2x)' equal to zero and attempt to solve:

Simplifying
1 + -2x = 0

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

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

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

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

Simplifying
x = 0.5

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 = {0.5, 1}

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