506=2x^2+24x+336

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Solution for 506=2x^2+24x+336 equation:


Simplifying
506 = 2x2 + 24x + 336

Reorder the terms:
506 = 336 + 24x + 2x2

Solving
506 = 336 + 24x + 2x2

Solving for variable 'x'.

Combine like terms: 506 + -336 = 170
170 + -24x + -2x2 = 336 + 24x + 2x2 + -336 + -24x + -2x2

Reorder the terms:
170 + -24x + -2x2 = 336 + -336 + 24x + -24x + 2x2 + -2x2

Combine like terms: 336 + -336 = 0
170 + -24x + -2x2 = 0 + 24x + -24x + 2x2 + -2x2
170 + -24x + -2x2 = 24x + -24x + 2x2 + -2x2

Combine like terms: 24x + -24x = 0
170 + -24x + -2x2 = 0 + 2x2 + -2x2
170 + -24x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
170 + -24x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(85 + -12x + -1x2) = 0

Factor a trinomial.
2((5 + -1x)(17 + x)) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5

Subproblem 2

Set the factor '(17 + x)' equal to zero and attempt to solve: Simplifying 17 + x = 0 Solving 17 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-17' to each side of the equation. 17 + -17 + x = 0 + -17 Combine like terms: 17 + -17 = 0 0 + x = 0 + -17 x = 0 + -17 Combine like terms: 0 + -17 = -17 x = -17 Simplifying x = -17

Solution

x = {5, -17}

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