x^2+6x+9-13(x+3)+42=0

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Solution for x^2+6x+9-13(x+3)+42=0 equation:


Simplifying
x2 + 6x + 9 + -13(x + 3) + 42 = 0

Reorder the terms:
x2 + 6x + 9 + -13(3 + x) + 42 = 0
x2 + 6x + 9 + (3 * -13 + x * -13) + 42 = 0
x2 + 6x + 9 + (-39 + -13x) + 42 = 0

Reorder the terms:
9 + -39 + 42 + 6x + -13x + x2 = 0

Combine like terms: 9 + -39 = -30
-30 + 42 + 6x + -13x + x2 = 0

Combine like terms: -30 + 42 = 12
12 + 6x + -13x + x2 = 0

Combine like terms: 6x + -13x = -7x
12 + -7x + x2 = 0

Solving
12 + -7x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(3 + -1x)(4 + -1x) = 0

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 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 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 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4

Solution

x = {3, 4}

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