2x^2-4x=6x+28

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Solution for 2x^2-4x=6x+28 equation: 


Simplifying
2x2 + -4x = 6x + 28

Reorder the terms:
-4x + 2x2 = 6x + 28

Reorder the terms:
-4x + 2x2 = 28 + 6x

Solving
-4x + 2x2 = 28 + 6x

Solving for variable 'x'.

Reorder the terms:
-28 + -4x + -6x + 2x2 = 28 + 6x + -28 + -6x

Combine like terms: -4x + -6x = -10x
-28 + -10x + 2x2 = 28 + 6x + -28 + -6x

Reorder the terms:
-28 + -10x + 2x2 = 28 + -28 + 6x + -6x

Combine like terms: 28 + -28 = 0
-28 + -10x + 2x2 = 0 + 6x + -6x
-28 + -10x + 2x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
-28 + -10x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-14 + -5x + x2) = 0

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

Ignore the factor 2.

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

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1x = 0 + 2
-1x = 0 + 2

Combine like terms: 0 + 2 = 2
-1x = 2

Divide each side by '-1'.
x = -2

Simplifying
x = -2

Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {-2, 7}

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