38=(x+3)+(x+9)+(x^2-2x)+(3x-2)

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Solution for 38=(x+3)+(x+9)+(x^2-2x)+(3x-2) equation:


Simplifying
38 = (x + 3) + (x + 9) + (x2 + -2x) + (3x + -2)

Reorder the terms:
38 = (3 + x) + (x + 9) + (x2 + -2x) + (3x + -2)

Remove parenthesis around (3 + x)
38 = 3 + x + (x + 9) + (x2 + -2x) + (3x + -2)

Reorder the terms:
38 = 3 + x + (9 + x) + (x2 + -2x) + (3x + -2)

Remove parenthesis around (9 + x)
38 = 3 + x + 9 + x + (x2 + -2x) + (3x + -2)

Reorder the terms:
38 = 3 + x + 9 + x + (-2x + x2) + (3x + -2)

Remove parenthesis around (-2x + x2)
38 = 3 + x + 9 + x + -2x + x2 + (3x + -2)

Reorder the terms:
38 = 3 + x + 9 + x + -2x + x2 + (-2 + 3x)

Remove parenthesis around (-2 + 3x)
38 = 3 + x + 9 + x + -2x + x2 + -2 + 3x

Reorder the terms:
38 = 3 + 9 + -2 + x + x + -2x + 3x + x2

Combine like terms: 3 + 9 = 12
38 = 12 + -2 + x + x + -2x + 3x + x2

Combine like terms: 12 + -2 = 10
38 = 10 + x + x + -2x + 3x + x2

Combine like terms: x + x = 2x
38 = 10 + 2x + -2x + 3x + x2

Combine like terms: 2x + -2x = 0
38 = 10 + 0 + 3x + x2
38 = 10 + 3x + x2

Solving
38 = 10 + 3x + x2

Solving for variable 'x'.

Combine like terms: 38 + -10 = 28
28 + -3x + -1x2 = 10 + 3x + x2 + -10 + -3x + -1x2

Reorder the terms:
28 + -3x + -1x2 = 10 + -10 + 3x + -3x + x2 + -1x2

Combine like terms: 10 + -10 = 0
28 + -3x + -1x2 = 0 + 3x + -3x + x2 + -1x2
28 + -3x + -1x2 = 3x + -3x + x2 + -1x2

Combine like terms: 3x + -3x = 0
28 + -3x + -1x2 = 0 + x2 + -1x2
28 + -3x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
28 + -3x + -1x2 = 0

Factor a trinomial.
(4 + -1x)(7 + x) = 0

Subproblem 1

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

Subproblem 2

Set the factor '(7 + x)' equal to zero and attempt to solve: Simplifying 7 + x = 0 Solving 7 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + x = 0 + -7 x = 0 + -7 Combine like terms: 0 + -7 = -7 x = -7 Simplifying x = -7

Solution

x = {4, -7}

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