-2x^2+x=-6x+20-5x^2

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Solution for -2x^2+x=-6x+20-5x^2 equation: 


Simplifying
-2x2 + x = -6x + 20 + -5x2

Reorder the terms:
x + -2x2 = -6x + 20 + -5x2

Reorder the terms:
x + -2x2 = 20 + -6x + -5x2

Solving
x + -2x2 = 20 + -6x + -5x2

Solving for variable 'x'.

Reorder the terms:
-20 + x + 6x + -2x2 + 5x2 = 20 + -6x + -5x2 + -20 + 6x + 5x2

Combine like terms: x + 6x = 7x
-20 + 7x + -2x2 + 5x2 = 20 + -6x + -5x2 + -20 + 6x + 5x2

Combine like terms: -2x2 + 5x2 = 3x2
-20 + 7x + 3x2 = 20 + -6x + -5x2 + -20 + 6x + 5x2

Reorder the terms:
-20 + 7x + 3x2 = 20 + -20 + -6x + 6x + -5x2 + 5x2

Combine like terms: 20 + -20 = 0
-20 + 7x + 3x2 = 0 + -6x + 6x + -5x2 + 5x2
-20 + 7x + 3x2 = -6x + 6x + -5x2 + 5x2

Combine like terms: -6x + 6x = 0
-20 + 7x + 3x2 = 0 + -5x2 + 5x2
-20 + 7x + 3x2 = -5x2 + 5x2

Combine like terms: -5x2 + 5x2 = 0
-20 + 7x + 3x2 = 0

Factor a trinomial.
(-4 + -1x)(5 + -3x) = 0


Subproblem 1
Set the factor '(-4 + -1x)' equal to zero and attempt to solve:

Simplifying
-4 + -1x = 0

Solving
-4 + -1x = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1x = 0 + 4

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

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

Divide each side by '-1'.
x = -4

Simplifying
x = -4

Subproblem 2
Set the factor '(5 + -3x)' equal to zero and attempt to solve:

Simplifying
5 + -3x = 0

Solving
5 + -3x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -3x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3x = 0 + -5
-3x = 0 + -5

Combine like terms: 0 + -5 = -5
-3x = -5

Divide each side by '-3'.
x = 1.666666667

Simplifying
x = 1.666666667
Solution
x = {-4, 1.666666667}

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