((x+7)*3)*((x+7)*3)=5184

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Solution for ((x+7)*3)*((x+7)*3)=5184 equation: 


Simplifying
((x + 7) * 3)((x + 7) * 3) = 5184

Reorder the terms:
((7 + x) * 3)((x + 7) * 3) = 5184

Reorder the terms for easier multiplication:
(3(7 + x))((x + 7) * 3) = 5184
((7 * 3 + x * 3))((x + 7) * 3) = 5184
((21 + 3x))((x + 7) * 3) = 5184

Reorder the terms:
(21 + 3x)((7 + x) * 3) = 5184

Reorder the terms for easier multiplication:
(21 + 3x)(3(7 + x)) = 5184
(21 + 3x)((7 * 3 + x * 3)) = 5184
(21 + 3x)((21 + 3x)) = 5184

Multiply (21 + 3x) * (21 + 3x)
(21(21 + 3x) + 3x * (21 + 3x)) = 5184
((21 * 21 + 3x * 21) + 3x * (21 + 3x)) = 5184
((441 + 63x) + 3x * (21 + 3x)) = 5184
(441 + 63x + (21 * 3x + 3x * 3x)) = 5184
(441 + 63x + (63x + 9x2)) = 5184

Combine like terms: 63x + 63x = 126x
(441 + 126x + 9x2) = 5184

Solving
441 + 126x + 9x2 = 5184

Solving for variable 'x'.

Reorder the terms:
441 + -5184 + 126x + 9x2 = 5184 + -5184

Combine like terms: 441 + -5184 = -4743
-4743 + 126x + 9x2 = 5184 + -5184

Combine like terms: 5184 + -5184 = 0
-4743 + 126x + 9x2 = 0

Factor out the Greatest Common Factor (GCF), '9'.
9(-527 + 14x + x2) = 0

Factor a trinomial.
9((-31 + -1x)(17 + -1x)) = 0

Ignore the factor 9.

Subproblem 1
Set the factor '(-31 + -1x)' equal to zero and attempt to solve:

Simplifying
-31 + -1x = 0

Solving
-31 + -1x = 0

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

Add '31' to each side of the equation.
-31 + 31 + -1x = 0 + 31

Combine like terms: -31 + 31 = 0
0 + -1x = 0 + 31
-1x = 0 + 31

Combine like terms: 0 + 31 = 31
-1x = 31

Divide each side by '-1'.
x = -31

Simplifying
x = -31

Subproblem 2
Set the factor '(17 + -1x)' equal to zero and attempt to solve:

Simplifying
17 + -1x = 0

Solving
17 + -1x = 0

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

Add '-17' to each side of the equation.
17 + -17 + -1x = 0 + -17

Combine like terms: 17 + -17 = 0
0 + -1x = 0 + -17
-1x = 0 + -17

Combine like terms: 0 + -17 = -17
-1x = -17

Divide each side by '-1'.
x = 17

Simplifying
x = 17
Solution
x = {-31, 17}

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