3(2x-5)(2x-5)-11(2x-5)=20

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Solution for 3(2x-5)(2x-5)-11(2x-5)=20 equation: 


Simplifying
3(2x + -5)(2x + -5) + -11(2x + -5) = 20

Reorder the terms:
3(-5 + 2x)(2x + -5) + -11(2x + -5) = 20

Reorder the terms:
3(-5 + 2x)(-5 + 2x) + -11(2x + -5) = 20

Multiply (-5 + 2x) * (-5 + 2x)
3(-5(-5 + 2x) + 2x * (-5 + 2x)) + -11(2x + -5) = 20
3((-5 * -5 + 2x * -5) + 2x * (-5 + 2x)) + -11(2x + -5) = 20
3((25 + -10x) + 2x * (-5 + 2x)) + -11(2x + -5) = 20
3(25 + -10x + (-5 * 2x + 2x * 2x)) + -11(2x + -5) = 20
3(25 + -10x + (-10x + 4x2)) + -11(2x + -5) = 20

Combine like terms: -10x + -10x = -20x
3(25 + -20x + 4x2) + -11(2x + -5) = 20
(25 * 3 + -20x * 3 + 4x2 * 3) + -11(2x + -5) = 20
(75 + -60x + 12x2) + -11(2x + -5) = 20

Reorder the terms:
75 + -60x + 12x2 + -11(-5 + 2x) = 20
75 + -60x + 12x2 + (-5 * -11 + 2x * -11) = 20
75 + -60x + 12x2 + (55 + -22x) = 20

Reorder the terms:
75 + 55 + -60x + -22x + 12x2 = 20

Combine like terms: 75 + 55 = 130
130 + -60x + -22x + 12x2 = 20

Combine like terms: -60x + -22x = -82x
130 + -82x + 12x2 = 20

Solving
130 + -82x + 12x2 = 20

Solving for variable 'x'.

Reorder the terms:
130 + -20 + -82x + 12x2 = 20 + -20

Combine like terms: 130 + -20 = 110
110 + -82x + 12x2 = 20 + -20

Combine like terms: 20 + -20 = 0
110 + -82x + 12x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(55 + -41x + 6x2) = 0

Factor a trinomial.
2((11 + -6x)(5 + -1x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(11 + -6x)' equal to zero and attempt to solve:

Simplifying
11 + -6x = 0

Solving
11 + -6x = 0

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

Add '-11' to each side of the equation.
11 + -11 + -6x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -6x = 0 + -11
-6x = 0 + -11

Combine like terms: 0 + -11 = -11
-6x = -11

Divide each side by '-6'.
x = 1.833333333

Simplifying
x = 1.833333333

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 = {1.833333333, 5}

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