20x^2+6x=4x+16+6x^2

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Solution for 20x^2+6x=4x+16+6x^2 equation: 


Simplifying
20x2 + 6x = 4x + 16 + 6x2

Reorder the terms:
6x + 20x2 = 4x + 16 + 6x2

Reorder the terms:
6x + 20x2 = 16 + 4x + 6x2

Solving
6x + 20x2 = 16 + 4x + 6x2

Solving for variable 'x'.

Reorder the terms:
-16 + 6x + -4x + 20x2 + -6x2 = 16 + 4x + 6x2 + -16 + -4x + -6x2

Combine like terms: 6x + -4x = 2x
-16 + 2x + 20x2 + -6x2 = 16 + 4x + 6x2 + -16 + -4x + -6x2

Combine like terms: 20x2 + -6x2 = 14x2
-16 + 2x + 14x2 = 16 + 4x + 6x2 + -16 + -4x + -6x2

Reorder the terms:
-16 + 2x + 14x2 = 16 + -16 + 4x + -4x + 6x2 + -6x2

Combine like terms: 16 + -16 = 0
-16 + 2x + 14x2 = 0 + 4x + -4x + 6x2 + -6x2
-16 + 2x + 14x2 = 4x + -4x + 6x2 + -6x2

Combine like terms: 4x + -4x = 0
-16 + 2x + 14x2 = 0 + 6x2 + -6x2
-16 + 2x + 14x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
-16 + 2x + 14x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-8 + x + 7x2) = 0

Factor a trinomial.
2((-8 + -7x)(1 + -1x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-8 + -7x)' equal to zero and attempt to solve:

Simplifying
-8 + -7x = 0

Solving
-8 + -7x = 0

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

Add '8' to each side of the equation.
-8 + 8 + -7x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -7x = 0 + 8
-7x = 0 + 8

Combine like terms: 0 + 8 = 8
-7x = 8

Divide each side by '-7'.
x = -1.142857143

Simplifying
x = -1.142857143

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 = {-1.142857143, 1}

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