3(2x-5)(2x-5)-(3x-7)(5-2x)=0

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Solution for 3(2x-5)(2x-5)-(3x-7)(5-2x)=0 equation: 


Simplifying
3(2x + -5)(2x + -5) + -1(3x + -7)(5 + -2x) = 0

Reorder the terms:
3(-5 + 2x)(2x + -5) + -1(3x + -7)(5 + -2x) = 0

Reorder the terms:
3(-5 + 2x)(-5 + 2x) + -1(3x + -7)(5 + -2x) = 0

Multiply (-5 + 2x) * (-5 + 2x)
3(-5(-5 + 2x) + 2x * (-5 + 2x)) + -1(3x + -7)(5 + -2x) = 0
3((-5 * -5 + 2x * -5) + 2x * (-5 + 2x)) + -1(3x + -7)(5 + -2x) = 0
3((25 + -10x) + 2x * (-5 + 2x)) + -1(3x + -7)(5 + -2x) = 0
3(25 + -10x + (-5 * 2x + 2x * 2x)) + -1(3x + -7)(5 + -2x) = 0
3(25 + -10x + (-10x + 4x2)) + -1(3x + -7)(5 + -2x) = 0

Combine like terms: -10x + -10x = -20x
3(25 + -20x + 4x2) + -1(3x + -7)(5 + -2x) = 0
(25 * 3 + -20x * 3 + 4x2 * 3) + -1(3x + -7)(5 + -2x) = 0
(75 + -60x + 12x2) + -1(3x + -7)(5 + -2x) = 0

Reorder the terms:
75 + -60x + 12x2 + -1(-7 + 3x)(5 + -2x) = 0

Multiply (-7 + 3x) * (5 + -2x)
75 + -60x + 12x2 + -1(-7(5 + -2x) + 3x * (5 + -2x)) = 0
75 + -60x + 12x2 + -1((5 * -7 + -2x * -7) + 3x * (5 + -2x)) = 0
75 + -60x + 12x2 + -1((-35 + 14x) + 3x * (5 + -2x)) = 0
75 + -60x + 12x2 + -1(-35 + 14x + (5 * 3x + -2x * 3x)) = 0
75 + -60x + 12x2 + -1(-35 + 14x + (15x + -6x2)) = 0

Combine like terms: 14x + 15x = 29x
75 + -60x + 12x2 + -1(-35 + 29x + -6x2) = 0
75 + -60x + 12x2 + (-35 * -1 + 29x * -1 + -6x2 * -1) = 0
75 + -60x + 12x2 + (35 + -29x + 6x2) = 0

Reorder the terms:
75 + 35 + -60x + -29x + 12x2 + 6x2 = 0

Combine like terms: 75 + 35 = 110
110 + -60x + -29x + 12x2 + 6x2 = 0

Combine like terms: -60x + -29x = -89x
110 + -89x + 12x2 + 6x2 = 0

Combine like terms: 12x2 + 6x2 = 18x2
110 + -89x + 18x2 = 0

Solving
110 + -89x + 18x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(22 + -9x)(5 + -2x) = 0


Subproblem 1
Set the factor '(22 + -9x)' equal to zero and attempt to solve:

Simplifying
22 + -9x = 0

Solving
22 + -9x = 0

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

Add '-22' to each side of the equation.
22 + -22 + -9x = 0 + -22

Combine like terms: 22 + -22 = 0
0 + -9x = 0 + -22
-9x = 0 + -22

Combine like terms: 0 + -22 = -22
-9x = -22

Divide each side by '-9'.
x = 2.444444444

Simplifying
x = 2.444444444

Subproblem 2
Set the factor '(5 + -2x)' equal to zero and attempt to solve:

Simplifying
5 + -2x = 0

Solving
5 + -2x = 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 + -2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2x = 0 + -5
-2x = 0 + -5

Combine like terms: 0 + -5 = -5
-2x = -5

Divide each side by '-2'.
x = 2.5

Simplifying
x = 2.5
Solution
x = {2.444444444, 2.5}

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