441=(2x+9)(2x+9)

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Solution for 441=(2x+9)(2x+9) equation: 


Simplifying
441 = (2x + 9)(2x + 9)

Reorder the terms:
441 = (9 + 2x)(2x + 9)

Reorder the terms:
441 = (9 + 2x)(9 + 2x)

Multiply (9 + 2x) * (9 + 2x)
441 = (9(9 + 2x) + 2x * (9 + 2x))
441 = ((9 * 9 + 2x * 9) + 2x * (9 + 2x))
441 = ((81 + 18x) + 2x * (9 + 2x))
441 = (81 + 18x + (9 * 2x + 2x * 2x))
441 = (81 + 18x + (18x + 4x2))

Combine like terms: 18x + 18x = 36x
441 = (81 + 36x + 4x2)

Solving
441 = 81 + 36x + 4x2

Solving for variable 'x'.

Combine like terms: 441 + -81 = 360
360 + -36x + -4x2 = 81 + 36x + 4x2 + -81 + -36x + -4x2

Reorder the terms:
360 + -36x + -4x2 = 81 + -81 + 36x + -36x + 4x2 + -4x2

Combine like terms: 81 + -81 = 0
360 + -36x + -4x2 = 0 + 36x + -36x + 4x2 + -4x2
360 + -36x + -4x2 = 36x + -36x + 4x2 + -4x2

Combine like terms: 36x + -36x = 0
360 + -36x + -4x2 = 0 + 4x2 + -4x2
360 + -36x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
360 + -36x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(90 + -9x + -1x2) = 0

Factor a trinomial.
4((6 + -1x)(15 + x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6

Subproblem 2
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
Solution
x = {6, -15}

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