(15+x+7)(x+7)=324

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Solution for (15+x+7)(x+7)=324 equation: 


Simplifying
(15 + x + 7)(x + 7) = 324

Reorder the terms:
(15 + 7 + x)(x + 7) = 324

Combine like terms: 15 + 7 = 22
(22 + x)(x + 7) = 324

Reorder the terms:
(22 + x)(7 + x) = 324

Multiply (22 + x) * (7 + x)
(22(7 + x) + x(7 + x)) = 324
((7 * 22 + x * 22) + x(7 + x)) = 324
((154 + 22x) + x(7 + x)) = 324
(154 + 22x + (7 * x + x * x)) = 324
(154 + 22x + (7x + x2)) = 324

Combine like terms: 22x + 7x = 29x
(154 + 29x + x2) = 324

Solving
154 + 29x + x2 = 324

Solving for variable 'x'.

Reorder the terms:
154 + -324 + 29x + x2 = 324 + -324

Combine like terms: 154 + -324 = -170
-170 + 29x + x2 = 324 + -324

Combine like terms: 324 + -324 = 0
-170 + 29x + x2 = 0

Factor a trinomial.
(-34 + -1x)(5 + -1x) = 0


Subproblem 1
Set the factor '(-34 + -1x)' equal to zero and attempt to solve:

Simplifying
-34 + -1x = 0

Solving
-34 + -1x = 0

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

Add '34' to each side of the equation.
-34 + 34 + -1x = 0 + 34

Combine like terms: -34 + 34 = 0
0 + -1x = 0 + 34
-1x = 0 + 34

Combine like terms: 0 + 34 = 34
-1x = 34

Divide each side by '-1'.
x = -34

Simplifying
x = -34

Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-34, 5}

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