(2x-1)(2x-1)-10(2x-1)+9=0

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Solution for (2x-1)(2x-1)-10(2x-1)+9=0 equation: 


Simplifying
(2x + -1)(2x + -1) + -10(2x + -1) + 9 = 0

Reorder the terms:
(-1 + 2x)(2x + -1) + -10(2x + -1) + 9 = 0

Reorder the terms:
(-1 + 2x)(-1 + 2x) + -10(2x + -1) + 9 = 0

Multiply (-1 + 2x) * (-1 + 2x)
(-1(-1 + 2x) + 2x * (-1 + 2x)) + -10(2x + -1) + 9 = 0
((-1 * -1 + 2x * -1) + 2x * (-1 + 2x)) + -10(2x + -1) + 9 = 0
((1 + -2x) + 2x * (-1 + 2x)) + -10(2x + -1) + 9 = 0
(1 + -2x + (-1 * 2x + 2x * 2x)) + -10(2x + -1) + 9 = 0
(1 + -2x + (-2x + 4x2)) + -10(2x + -1) + 9 = 0

Combine like terms: -2x + -2x = -4x
(1 + -4x + 4x2) + -10(2x + -1) + 9 = 0

Reorder the terms:
1 + -4x + 4x2 + -10(-1 + 2x) + 9 = 0
1 + -4x + 4x2 + (-1 * -10 + 2x * -10) + 9 = 0
1 + -4x + 4x2 + (10 + -20x) + 9 = 0

Reorder the terms:
1 + 10 + 9 + -4x + -20x + 4x2 = 0

Combine like terms: 1 + 10 = 11
11 + 9 + -4x + -20x + 4x2 = 0

Combine like terms: 11 + 9 = 20
20 + -4x + -20x + 4x2 = 0

Combine like terms: -4x + -20x = -24x
20 + -24x + 4x2 = 0

Solving
20 + -24x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(5 + -6x + x2) = 0

Factor a trinomial.
4((1 + -1x)(5 + -1x)) = 0

Ignore the factor 4.

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 '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {1, 5}

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