8x^2+3x+1=3x^2-3x

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Solution for 8x^2+3x+1=3x^2-3x equation: 


Simplifying
8x2 + 3x + 1 = 3x2 + -3x

Reorder the terms:
1 + 3x + 8x2 = 3x2 + -3x

Reorder the terms:
1 + 3x + 8x2 = -3x + 3x2

Solving
1 + 3x + 8x2 = -3x + 3x2

Solving for variable 'x'.

Reorder the terms:
1 + 3x + 3x + 8x2 + -3x2 = -3x + 3x2 + 3x + -3x2

Combine like terms: 3x + 3x = 6x
1 + 6x + 8x2 + -3x2 = -3x + 3x2 + 3x + -3x2

Combine like terms: 8x2 + -3x2 = 5x2
1 + 6x + 5x2 = -3x + 3x2 + 3x + -3x2

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

Combine like terms: -3x + 3x = 0
1 + 6x + 5x2 = 0 + 3x2 + -3x2
1 + 6x + 5x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
1 + 6x + 5x2 = 0

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


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 + 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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