2x^2-10=2x+14

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Solution for 2x^2-10=2x+14 equation: 


Simplifying
2x2 + -10 = 2x + 14

Reorder the terms:
-10 + 2x2 = 2x + 14

Reorder the terms:
-10 + 2x2 = 14 + 2x

Solving
-10 + 2x2 = 14 + 2x

Solving for variable 'x'.

Reorder the terms:
-10 + -14 + -2x + 2x2 = 14 + 2x + -14 + -2x

Combine like terms: -10 + -14 = -24
-24 + -2x + 2x2 = 14 + 2x + -14 + -2x

Reorder the terms:
-24 + -2x + 2x2 = 14 + -14 + 2x + -2x

Combine like terms: 14 + -14 = 0
-24 + -2x + 2x2 = 0 + 2x + -2x
-24 + -2x + 2x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-24 + -2x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-12 + -1x + x2) = 0

Factor a trinomial.
2((-3 + -1x)(4 + -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 '(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
Solution
x = {-3, 4}

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