6(x+9)*(x+9)=24

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Solution for 6(x+9)*(x+9)=24 equation: 


Simplifying
6(x + 9)(x + 9) = 24

Reorder the terms:
6(9 + x)(x + 9) = 24

Reorder the terms:
6(9 + x)(9 + x) = 24

Multiply (9 + x) * (9 + x)
6(9(9 + x) + x(9 + x)) = 24
6((9 * 9 + x * 9) + x(9 + x)) = 24
6((81 + 9x) + x(9 + x)) = 24
6(81 + 9x + (9 * x + x * x)) = 24
6(81 + 9x + (9x + x2)) = 24

Combine like terms: 9x + 9x = 18x
6(81 + 18x + x2) = 24
(81 * 6 + 18x * 6 + x2 * 6) = 24
(486 + 108x + 6x2) = 24

Solving
486 + 108x + 6x2 = 24

Solving for variable 'x'.

Reorder the terms:
486 + -24 + 108x + 6x2 = 24 + -24

Combine like terms: 486 + -24 = 462
462 + 108x + 6x2 = 24 + -24

Combine like terms: 24 + -24 = 0
462 + 108x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(77 + 18x + x2) = 0

Factor a trinomial.
6((11 + x)(7 + x)) = 0

Ignore the factor 6.

Subproblem 1
Set the factor '(11 + x)' equal to zero and attempt to solve:

Simplifying
11 + x = 0

Solving
11 + x = 0

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

Add '-11' to each side of the equation.
11 + -11 + x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + x = 0 + -11
x = 0 + -11

Combine like terms: 0 + -11 = -11
x = -11

Simplifying
x = -11

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 = {-11, -7}

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