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

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


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

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

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

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

Solving for variable 'x'.

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

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

Combine like terms: 1x + 3x = 4x
1 + 4x + -5x2 = 2 + -3x + 5x2 + -2 + 3x + -5x2

Reorder the terms:
1 + 4x + -5x2 = 2 + -2 + -3x + 3x + 5x2 + -5x2

Combine like terms: 2 + -2 = 0
1 + 4x + -5x2 = 0 + -3x + 3x + 5x2 + -5x2
1 + 4x + -5x2 = -3x + 3x + 5x2 + -5x2

Combine like terms: -3x + 3x = 0
1 + 4x + -5x2 = 0 + 5x2 + -5x2
1 + 4x + -5x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
1 + 4x + -5x2 = 0

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


Subproblem 1
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

Subproblem 2
Set the factor '(1 + 5x)' equal to zero and attempt to solve:

Simplifying
1 + 5x = 0

Solving
1 + 5x = 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 + 5x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 5x = 0 + -1
5x = 0 + -1

Combine like terms: 0 + -1 = -1
5x = -1

Divide each side by '5'.
x = -0.2

Simplifying
x = -0.2
Solution
x = {1, -0.2}

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