(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((-7 + -1x)(10 + -1x)) = 0

Ignore the factor 4.

Subproblem 1
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

Subproblem 2
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
Solution
x = {-7, 10}

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