x^2+7x+24=-2x+4

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Solution for x^2+7x+24=-2x+4 equation:


Simplifying
x2 + 7x + 24 = -2x + 4

Reorder the terms:
24 + 7x + x2 = -2x + 4

Reorder the terms:
24 + 7x + x2 = 4 + -2x

Solving
24 + 7x + x2 = 4 + -2x

Solving for variable 'x'.

Reorder the terms:
24 + -4 + 7x + 2x + x2 = 4 + -2x + -4 + 2x

Combine like terms: 24 + -4 = 20
20 + 7x + 2x + x2 = 4 + -2x + -4 + 2x

Combine like terms: 7x + 2x = 9x
20 + 9x + x2 = 4 + -2x + -4 + 2x

Reorder the terms:
20 + 9x + x2 = 4 + -4 + -2x + 2x

Combine like terms: 4 + -4 = 0
20 + 9x + x2 = 0 + -2x + 2x
20 + 9x + x2 = -2x + 2x

Combine like terms: -2x + 2x = 0
20 + 9x + x2 = 0

Factor a trinomial.
(5 + x)(4 + x) = 0

Subproblem 1

Set the factor '(5 + x)' equal to zero and attempt to solve: Simplifying 5 + x = 0 Solving 5 + x = 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 + x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + x = 0 + -5 x = 0 + -5 Combine like terms: 0 + -5 = -5 x = -5 Simplifying x = -5

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 = {-5, -4}

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