5x^2+2x-4=2x^2+12

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Solution for 5x^2+2x-4=2x^2+12 equation: 


Simplifying
5x2 + 2x + -4 = 2x2 + 12

Reorder the terms:
-4 + 2x + 5x2 = 2x2 + 12

Reorder the terms:
-4 + 2x + 5x2 = 12 + 2x2

Solving
-4 + 2x + 5x2 = 12 + 2x2

Solving for variable 'x'.

Reorder the terms:
-4 + -12 + 2x + 5x2 + -2x2 = 12 + 2x2 + -12 + -2x2

Combine like terms: -4 + -12 = -16
-16 + 2x + 5x2 + -2x2 = 12 + 2x2 + -12 + -2x2

Combine like terms: 5x2 + -2x2 = 3x2
-16 + 2x + 3x2 = 12 + 2x2 + -12 + -2x2

Reorder the terms:
-16 + 2x + 3x2 = 12 + -12 + 2x2 + -2x2

Combine like terms: 12 + -12 = 0
-16 + 2x + 3x2 = 0 + 2x2 + -2x2
-16 + 2x + 3x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-16 + 2x + 3x2 = 0

Factor a trinomial.
(-8 + -3x)(2 + -1x) = 0


Subproblem 1
Set the factor '(-8 + -3x)' equal to zero and attempt to solve:

Simplifying
-8 + -3x = 0

Solving
-8 + -3x = 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 + -3x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -3x = 0 + 8
-3x = 0 + 8

Combine like terms: 0 + 8 = 8
-3x = 8

Divide each side by '-3'.
x = -2.666666667

Simplifying
x = -2.666666667

Subproblem 2
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
Solution
x = {-2.666666667, 2}

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