(2x-3)(2x-3)-x=0

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Solution for (2x-3)(2x-3)-x=0 equation: 


Simplifying
(2x + -3)(2x + -3) + -1x = 0

Reorder the terms:
(-3 + 2x)(2x + -3) + -1x = 0

Reorder the terms:
(-3 + 2x)(-3 + 2x) + -1x = 0

Multiply (-3 + 2x) * (-3 + 2x)
(-3(-3 + 2x) + 2x * (-3 + 2x)) + -1x = 0
((-3 * -3 + 2x * -3) + 2x * (-3 + 2x)) + -1x = 0
((9 + -6x) + 2x * (-3 + 2x)) + -1x = 0
(9 + -6x + (-3 * 2x + 2x * 2x)) + -1x = 0
(9 + -6x + (-6x + 4x2)) + -1x = 0

Combine like terms: -6x + -6x = -12x
(9 + -12x + 4x2) + -1x = 0

Reorder the terms:
9 + -12x + -1x + 4x2 = 0

Combine like terms: -12x + -1x = -13x
9 + -13x + 4x2 = 0

Solving
9 + -13x + 4x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(1 + -1x)(9 + -4x) = 0


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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1

Subproblem 2
Set the factor '(9 + -4x)' equal to zero and attempt to solve:

Simplifying
9 + -4x = 0

Solving
9 + -4x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -4x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -4x = 0 + -9
-4x = 0 + -9

Combine like terms: 0 + -9 = -9
-4x = -9

Divide each side by '-4'.
x = 2.25

Simplifying
x = 2.25
Solution
x = {1, 2.25}

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