(x+7)(x+7)+15(x+7)+56=0

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Solution for (x+7)(x+7)+15(x+7)+56=0 equation: 


Simplifying
(x + 7)(x + 7) + 15(x + 7) + 56 = 0

Reorder the terms:
(7 + x)(x + 7) + 15(x + 7) + 56 = 0

Reorder the terms:
(7 + x)(7 + x) + 15(x + 7) + 56 = 0

Multiply (7 + x) * (7 + x)
(7(7 + x) + x(7 + x)) + 15(x + 7) + 56 = 0
((7 * 7 + x * 7) + x(7 + x)) + 15(x + 7) + 56 = 0
((49 + 7x) + x(7 + x)) + 15(x + 7) + 56 = 0
(49 + 7x + (7 * x + x * x)) + 15(x + 7) + 56 = 0
(49 + 7x + (7x + x2)) + 15(x + 7) + 56 = 0

Combine like terms: 7x + 7x = 14x
(49 + 14x + x2) + 15(x + 7) + 56 = 0

Reorder the terms:
49 + 14x + x2 + 15(7 + x) + 56 = 0
49 + 14x + x2 + (7 * 15 + x * 15) + 56 = 0
49 + 14x + x2 + (105 + 15x) + 56 = 0

Reorder the terms:
49 + 105 + 56 + 14x + 15x + x2 = 0

Combine like terms: 49 + 105 = 154
154 + 56 + 14x + 15x + x2 = 0

Combine like terms: 154 + 56 = 210
210 + 14x + 15x + x2 = 0

Combine like terms: 14x + 15x = 29x
210 + 29x + x2 = 0

Solving
210 + 29x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(15 + x)(14 + x) = 0


Subproblem 1
Set the factor '(15 + x)' equal to zero and attempt to solve:

Simplifying
15 + x = 0

Solving
15 + x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-15' to each side of the equation.
15 + -15 + x = 0 + -15

Combine like terms: 15 + -15 = 0
0 + x = 0 + -15
x = 0 + -15

Combine like terms: 0 + -15 = -15
x = -15

Simplifying
x = -15

Subproblem 2
Set the factor '(14 + x)' equal to zero and attempt to solve:

Simplifying
14 + x = 0

Solving
14 + x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-14' to each side of the equation.
14 + -14 + x = 0 + -14

Combine like terms: 14 + -14 = 0
0 + x = 0 + -14
x = 0 + -14

Combine like terms: 0 + -14 = -14
x = -14

Simplifying
x = -14
Solution
x = {-15, -14}

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