5x^2+3x+1=10-3x-3x^2

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Solution for 5x^2+3x+1=10-3x-3x^2 equation: 


Simplifying
5x2 + 3x + 1 = 10 + -3x + -3x2

Reorder the terms:
1 + 3x + 5x2 = 10 + -3x + -3x2

Solving
1 + 3x + 5x2 = 10 + -3x + -3x2

Solving for variable 'x'.

Reorder the terms:
1 + -10 + 3x + 3x + 5x2 + 3x2 = 10 + -3x + -3x2 + -10 + 3x + 3x2

Combine like terms: 1 + -10 = -9
-9 + 3x + 3x + 5x2 + 3x2 = 10 + -3x + -3x2 + -10 + 3x + 3x2

Combine like terms: 3x + 3x = 6x
-9 + 6x + 5x2 + 3x2 = 10 + -3x + -3x2 + -10 + 3x + 3x2

Combine like terms: 5x2 + 3x2 = 8x2
-9 + 6x + 8x2 = 10 + -3x + -3x2 + -10 + 3x + 3x2

Reorder the terms:
-9 + 6x + 8x2 = 10 + -10 + -3x + 3x + -3x2 + 3x2

Combine like terms: 10 + -10 = 0
-9 + 6x + 8x2 = 0 + -3x + 3x + -3x2 + 3x2
-9 + 6x + 8x2 = -3x + 3x + -3x2 + 3x2

Combine like terms: -3x + 3x = 0
-9 + 6x + 8x2 = 0 + -3x2 + 3x2
-9 + 6x + 8x2 = -3x2 + 3x2

Combine like terms: -3x2 + 3x2 = 0
-9 + 6x + 8x2 = 0

Factor a trinomial.
(-3 + -2x)(3 + -4x) = 0


Subproblem 1
Set the factor '(-3 + -2x)' equal to zero and attempt to solve:

Simplifying
-3 + -2x = 0

Solving
-3 + -2x = 0

Move all terms containing x to the left, all other terms to the right.

Add '3' to each side of the equation.
-3 + 3 + -2x = 0 + 3

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

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

Divide each side by '-2'.
x = -1.5

Simplifying
x = -1.5

Subproblem 2
Set the factor '(3 + -4x)' equal to zero and attempt to solve:

Simplifying
3 + -4x = 0

Solving
3 + -4x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + -4x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4x = 0 + -3
-4x = 0 + -3

Combine like terms: 0 + -3 = -3
-4x = -3

Divide each side by '-4'.
x = 0.75

Simplifying
x = 0.75
Solution
x = {-1.5, 0.75}

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