2x(x+1)=420

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Solution for 2x(x+1)=420 equation:


Simplifying
2x(x + 1) = 420

Reorder the terms:
2x(1 + x) = 420
(1 * 2x + x * 2x) = 420
(2x + 2x2) = 420

Solving
2x + 2x2 = 420

Solving for variable 'x'.

Reorder the terms:
-420 + 2x + 2x2 = 420 + -420

Combine like terms: 420 + -420 = 0
-420 + 2x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-210 + x + x2) = 0

Factor a trinomial.
2((-15 + -1x)(14 + -1x)) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-15 + -1x)' equal to zero and attempt to solve: Simplifying -15 + -1x = 0 Solving -15 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + -1x = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -1x = 0 + 15 -1x = 0 + 15 Combine like terms: 0 + 15 = 15 -1x = 15 Divide each side by '-1'. x = -15 Simplifying x = -15

Subproblem 2

Set the factor '(14 + -1x)' equal to zero and attempt to solve: Simplifying 14 + -1x = 0 Solving 14 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + -1x = 0 + -14 Combine like terms: 14 + -14 = 0 0 + -1x = 0 + -14 -1x = 0 + -14 Combine like terms: 0 + -14 = -14 -1x = -14 Divide each side by '-1'. x = 14 Simplifying x = 14

Solution

x = {-15, 14}

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