2x^2+2x=12x+48

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Solution for 2x^2+2x=12x+48 equation: 


Simplifying
2x2 + 2x = 12x + 48

Reorder the terms:
2x + 2x2 = 12x + 48

Reorder the terms:
2x + 2x2 = 48 + 12x

Solving
2x + 2x2 = 48 + 12x

Solving for variable 'x'.

Reorder the terms:
-48 + 2x + -12x + 2x2 = 48 + 12x + -48 + -12x

Combine like terms: 2x + -12x = -10x
-48 + -10x + 2x2 = 48 + 12x + -48 + -12x

Reorder the terms:
-48 + -10x + 2x2 = 48 + -48 + 12x + -12x

Combine like terms: 48 + -48 = 0
-48 + -10x + 2x2 = 0 + 12x + -12x
-48 + -10x + 2x2 = 12x + -12x

Combine like terms: 12x + -12x = 0
-48 + -10x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-24 + -5x + x2) = 0

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

Ignore the factor 2.

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

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 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 + -1x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1x = 0 + 3
-1x = 0 + 3

Combine like terms: 0 + 3 = 3
-1x = 3

Divide each side by '-1'.
x = -3

Simplifying
x = -3

Subproblem 2
Set the factor '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 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 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {-3, 8}

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