(x^2+7x)+42=3(7-x)

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Solution for (x^2+7x)+42=3(7-x) equation: 


Simplifying
(x2 + 7x) + 42 = 3(7 + -1x)

Reorder the terms:
(7x + x2) + 42 = 3(7 + -1x)

Remove parenthesis around (7x + x2)
7x + x2 + 42 = 3(7 + -1x)

Reorder the terms:
42 + 7x + x2 = 3(7 + -1x)
42 + 7x + x2 = (7 * 3 + -1x * 3)
42 + 7x + x2 = (21 + -3x)

Solving
42 + 7x + x2 = 21 + -3x

Solving for variable 'x'.

Reorder the terms:
42 + -21 + 7x + 3x + x2 = 21 + -3x + -21 + 3x

Combine like terms: 42 + -21 = 21
21 + 7x + 3x + x2 = 21 + -3x + -21 + 3x

Combine like terms: 7x + 3x = 10x
21 + 10x + x2 = 21 + -3x + -21 + 3x

Reorder the terms:
21 + 10x + x2 = 21 + -21 + -3x + 3x

Combine like terms: 21 + -21 = 0
21 + 10x + x2 = 0 + -3x + 3x
21 + 10x + x2 = -3x + 3x

Combine like terms: -3x + 3x = 0
21 + 10x + x2 = 0

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


Subproblem 1
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

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 = {-7, -3}

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