x^2+19x+29=5x-4

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Solution for x^2+19x+29=5x-4 equation:


Simplifying
x2 + 19x + 29 = 5x + -4

Reorder the terms:
29 + 19x + x2 = 5x + -4

Reorder the terms:
29 + 19x + x2 = -4 + 5x

Solving
29 + 19x + x2 = -4 + 5x

Solving for variable 'x'.

Reorder the terms:
29 + 4 + 19x + -5x + x2 = -4 + 5x + 4 + -5x

Combine like terms: 29 + 4 = 33
33 + 19x + -5x + x2 = -4 + 5x + 4 + -5x

Combine like terms: 19x + -5x = 14x
33 + 14x + x2 = -4 + 5x + 4 + -5x

Reorder the terms:
33 + 14x + x2 = -4 + 4 + 5x + -5x

Combine like terms: -4 + 4 = 0
33 + 14x + x2 = 0 + 5x + -5x
33 + 14x + x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
33 + 14x + x2 = 0

Factor a trinomial.
(11 + x)(3 + x) = 0

Subproblem 1

Set the factor '(11 + x)' equal to zero and attempt to solve: Simplifying 11 + x = 0 Solving 11 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + x = 0 + -11 Combine like terms: 11 + -11 = 0 0 + x = 0 + -11 x = 0 + -11 Combine like terms: 0 + -11 = -11 x = -11 Simplifying x = -11

Subproblem 2

Set the factor '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 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 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Simplifying x = -3

Solution

x = {-11, -3}

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