(2x+9)(2x+9)=225

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Solution for (2x+9)(2x+9)=225 equation:


Simplifying
(2x + 9)(2x + 9) = 225

Reorder the terms:
(9 + 2x)(2x + 9) = 225

Reorder the terms:
(9 + 2x)(9 + 2x) = 225

Multiply (9 + 2x) * (9 + 2x)
(9(9 + 2x) + 2x * (9 + 2x)) = 225
((9 * 9 + 2x * 9) + 2x * (9 + 2x)) = 225
((81 + 18x) + 2x * (9 + 2x)) = 225
(81 + 18x + (9 * 2x + 2x * 2x)) = 225
(81 + 18x + (18x + 4x2)) = 225

Combine like terms: 18x + 18x = 36x
(81 + 36x + 4x2) = 225

Solving
81 + 36x + 4x2 = 225

Solving for variable 'x'.

Reorder the terms:
81 + -225 + 36x + 4x2 = 225 + -225

Combine like terms: 81 + -225 = -144
-144 + 36x + 4x2 = 225 + -225

Combine like terms: 225 + -225 = 0
-144 + 36x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-36 + 9x + x2) = 0

Factor a trinomial.
4((-12 + -1x)(3 + -1x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-12 + -1x)' equal to zero and attempt to solve:

Simplifying
-12 + -1x = 0

Solving
-12 + -1x = 0

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

Add '12' to each side of the equation.
-12 + 12 + -1x = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -1x = 0 + 12
-1x = 0 + 12

Combine like terms: 0 + 12 = 12
-1x = 12

Divide each side by '-1'.
x = -12

Simplifying
x = -12

Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-12, 3}

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