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

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


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

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

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

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

Combine like terms: -2x + -2x = -4x
9(1 + -4x + 4x2) + 2 = -9(2x + -1)
(1 * 9 + -4x * 9 + 4x2 * 9) + 2 = -9(2x + -1)
(9 + -36x + 36x2) + 2 = -9(2x + -1)

Reorder the terms:
9 + 2 + -36x + 36x2 = -9(2x + -1)

Combine like terms: 9 + 2 = 11
11 + -36x + 36x2 = -9(2x + -1)

Reorder the terms:
11 + -36x + 36x2 = -9(-1 + 2x)
11 + -36x + 36x2 = (-1 * -9 + 2x * -9)
11 + -36x + 36x2 = (9 + -18x)

Solving
11 + -36x + 36x2 = 9 + -18x

Solving for variable 'x'.

Reorder the terms:
11 + -9 + -36x + 18x + 36x2 = 9 + -18x + -9 + 18x

Combine like terms: 11 + -9 = 2
2 + -36x + 18x + 36x2 = 9 + -18x + -9 + 18x

Combine like terms: -36x + 18x = -18x
2 + -18x + 36x2 = 9 + -18x + -9 + 18x

Reorder the terms:
2 + -18x + 36x2 = 9 + -9 + -18x + 18x

Combine like terms: 9 + -9 = 0
2 + -18x + 36x2 = 0 + -18x + 18x
2 + -18x + 36x2 = -18x + 18x

Combine like terms: -18x + 18x = 0
2 + -18x + 36x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + -9x + 18x2) = 0

Factor a trinomial.
2((1 + -6x)(1 + -3x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(1 + -6x)' equal to zero and attempt to solve:

Simplifying
1 + -6x = 0

Solving
1 + -6x = 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 + -6x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -6x = 0 + -1
-6x = 0 + -1

Combine like terms: 0 + -1 = -1
-6x = -1

Divide each side by '-6'.
x = 0.1666666667

Simplifying
x = 0.1666666667

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

Simplifying
1 + -3x = 0

Solving
1 + -3x = 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 + -3x = 0 + -1

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

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

Divide each side by '-3'.
x = 0.3333333333

Simplifying
x = 0.3333333333
Solution
x = {0.1666666667, 0.3333333333}

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