(3x-5)(4x-7)+(3x-2)(5x-4)=2

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Solution for (3x-5)(4x-7)+(3x-2)(5x-4)=2 equation: 


Simplifying
(3x + -5)(4x + -7) + (3x + -2)(5x + -4) = 2

Reorder the terms:
(-5 + 3x)(4x + -7) + (3x + -2)(5x + -4) = 2

Reorder the terms:
(-5 + 3x)(-7 + 4x) + (3x + -2)(5x + -4) = 2

Multiply (-5 + 3x) * (-7 + 4x)
(-5(-7 + 4x) + 3x * (-7 + 4x)) + (3x + -2)(5x + -4) = 2
((-7 * -5 + 4x * -5) + 3x * (-7 + 4x)) + (3x + -2)(5x + -4) = 2
((35 + -20x) + 3x * (-7 + 4x)) + (3x + -2)(5x + -4) = 2
(35 + -20x + (-7 * 3x + 4x * 3x)) + (3x + -2)(5x + -4) = 2
(35 + -20x + (-21x + 12x2)) + (3x + -2)(5x + -4) = 2

Combine like terms: -20x + -21x = -41x
(35 + -41x + 12x2) + (3x + -2)(5x + -4) = 2

Reorder the terms:
35 + -41x + 12x2 + (-2 + 3x)(5x + -4) = 2

Reorder the terms:
35 + -41x + 12x2 + (-2 + 3x)(-4 + 5x) = 2

Multiply (-2 + 3x) * (-4 + 5x)
35 + -41x + 12x2 + (-2(-4 + 5x) + 3x * (-4 + 5x)) = 2
35 + -41x + 12x2 + ((-4 * -2 + 5x * -2) + 3x * (-4 + 5x)) = 2
35 + -41x + 12x2 + ((8 + -10x) + 3x * (-4 + 5x)) = 2
35 + -41x + 12x2 + (8 + -10x + (-4 * 3x + 5x * 3x)) = 2
35 + -41x + 12x2 + (8 + -10x + (-12x + 15x2)) = 2

Combine like terms: -10x + -12x = -22x
35 + -41x + 12x2 + (8 + -22x + 15x2) = 2

Reorder the terms:
35 + 8 + -41x + -22x + 12x2 + 15x2 = 2

Combine like terms: 35 + 8 = 43
43 + -41x + -22x + 12x2 + 15x2 = 2

Combine like terms: -41x + -22x = -63x
43 + -63x + 12x2 + 15x2 = 2

Combine like terms: 12x2 + 15x2 = 27x2
43 + -63x + 27x2 = 2

Solving
43 + -63x + 27x2 = 2

Solving for variable 'x'.

Reorder the terms:
43 + -2 + -63x + 27x2 = 2 + -2

Combine like terms: 43 + -2 = 41
41 + -63x + 27x2 = 2 + -2

Combine like terms: 2 + -2 = 0
41 + -63x + 27x2 = 0

Begin completing the square.  Divide all terms by
27 the coefficient of the squared term: 

Divide each side by '27'.
1.518518519 + -2.333333333x + x2 = 0

Move the constant term to the right:

Add '-1.518518519' to each side of the equation.
1.518518519 + -2.333333333x + -1.518518519 + x2 = 0 + -1.518518519

Reorder the terms:
1.518518519 + -1.518518519 + -2.333333333x + x2 = 0 + -1.518518519

Combine like terms: 1.518518519 + -1.518518519 = 0.000000000
0.000000000 + -2.333333333x + x2 = 0 + -1.518518519
-2.333333333x + x2 = 0 + -1.518518519

Combine like terms: 0 + -1.518518519 = -1.518518519
-2.333333333x + x2 = -1.518518519

The x term is -2.333333333x.  Take half its coefficient (-1.166666667).
Square it (1.361111112) and add it to both sides.

Add '1.361111112' to each side of the equation.
-2.333333333x + 1.361111112 + x2 = -1.518518519 + 1.361111112

Reorder the terms:
1.361111112 + -2.333333333x + x2 = -1.518518519 + 1.361111112

Combine like terms: -1.518518519 + 1.361111112 = -0.157407407
1.361111112 + -2.333333333x + x2 = -0.157407407

Factor a perfect square on the left side:
(x + -1.166666667)(x + -1.166666667) = -0.157407407

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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