(2x+3)(2x+3)=289

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Solution for (2x+3)(2x+3)=289 equation: 


Simplifying
(2x + 3)(2x + 3) = 289

Reorder the terms:
(3 + 2x)(2x + 3) = 289

Reorder the terms:
(3 + 2x)(3 + 2x) = 289

Multiply (3 + 2x) * (3 + 2x)
(3(3 + 2x) + 2x * (3 + 2x)) = 289
((3 * 3 + 2x * 3) + 2x * (3 + 2x)) = 289
((9 + 6x) + 2x * (3 + 2x)) = 289
(9 + 6x + (3 * 2x + 2x * 2x)) = 289
(9 + 6x + (6x + 4x2)) = 289

Combine like terms: 6x + 6x = 12x
(9 + 12x + 4x2) = 289

Solving
9 + 12x + 4x2 = 289

Solving for variable 'x'.

Reorder the terms:
9 + -289 + 12x + 4x2 = 289 + -289

Combine like terms: 9 + -289 = -280
-280 + 12x + 4x2 = 289 + -289

Combine like terms: 289 + -289 = 0
-280 + 12x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-70 + 3x + x2) = 0

Factor a trinomial.
4((-10 + -1x)(7 + -1x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-10 + -1x)' equal to zero and attempt to solve:

Simplifying
-10 + -1x = 0

Solving
-10 + -1x = 0

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

Add '10' to each side of the equation.
-10 + 10 + -1x = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -1x = 0 + 10
-1x = 0 + 10

Combine like terms: 0 + 10 = 10
-1x = 10

Divide each side by '-1'.
x = -10

Simplifying
x = -10

Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 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 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {-10, 7}

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