0=2x^2-24+2x

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Solution for 0=2x^2-24+2x equation:


Simplifying
0 = 2x2 + -24 + 2x

Reorder the terms:
0 = -24 + 2x + 2x2

Solving
0 = -24 + 2x + 2x2

Solving for variable 'x'.

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

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

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

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

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

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

Factor a trinomial.
2((3 + -1x)(4 + x)) = 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 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 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 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 x = -4 Simplifying x = -4

Solution

x = {3, -4}

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