(4x-5)(3x-1)-(2x-7)(6x+5)-1=0

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Solution for (4x-5)(3x-1)-(2x-7)(6x+5)-1=0 equation: 


Simplifying
(4x + -5)(3x + -1) + -1(2x + -7)(6x + 5) + -1 = 0

Reorder the terms:
(-5 + 4x)(3x + -1) + -1(2x + -7)(6x + 5) + -1 = 0

Reorder the terms:
(-5 + 4x)(-1 + 3x) + -1(2x + -7)(6x + 5) + -1 = 0

Multiply (-5 + 4x) * (-1 + 3x)
(-5(-1 + 3x) + 4x * (-1 + 3x)) + -1(2x + -7)(6x + 5) + -1 = 0
((-1 * -5 + 3x * -5) + 4x * (-1 + 3x)) + -1(2x + -7)(6x + 5) + -1 = 0
((5 + -15x) + 4x * (-1 + 3x)) + -1(2x + -7)(6x + 5) + -1 = 0
(5 + -15x + (-1 * 4x + 3x * 4x)) + -1(2x + -7)(6x + 5) + -1 = 0
(5 + -15x + (-4x + 12x2)) + -1(2x + -7)(6x + 5) + -1 = 0

Combine like terms: -15x + -4x = -19x
(5 + -19x + 12x2) + -1(2x + -7)(6x + 5) + -1 = 0

Reorder the terms:
5 + -19x + 12x2 + -1(-7 + 2x)(6x + 5) + -1 = 0

Reorder the terms:
5 + -19x + 12x2 + -1(-7 + 2x)(5 + 6x) + -1 = 0

Multiply (-7 + 2x) * (5 + 6x)
5 + -19x + 12x2 + -1(-7(5 + 6x) + 2x * (5 + 6x)) + -1 = 0
5 + -19x + 12x2 + -1((5 * -7 + 6x * -7) + 2x * (5 + 6x)) + -1 = 0
5 + -19x + 12x2 + -1((-35 + -42x) + 2x * (5 + 6x)) + -1 = 0
5 + -19x + 12x2 + -1(-35 + -42x + (5 * 2x + 6x * 2x)) + -1 = 0
5 + -19x + 12x2 + -1(-35 + -42x + (10x + 12x2)) + -1 = 0

Combine like terms: -42x + 10x = -32x
5 + -19x + 12x2 + -1(-35 + -32x + 12x2) + -1 = 0
5 + -19x + 12x2 + (-35 * -1 + -32x * -1 + 12x2 * -1) + -1 = 0
5 + -19x + 12x2 + (35 + 32x + -12x2) + -1 = 0

Reorder the terms:
5 + 35 + -1 + -19x + 32x + 12x2 + -12x2 = 0

Combine like terms: 5 + 35 = 40
40 + -1 + -19x + 32x + 12x2 + -12x2 = 0

Combine like terms: 40 + -1 = 39
39 + -19x + 32x + 12x2 + -12x2 = 0

Combine like terms: -19x + 32x = 13x
39 + 13x + 12x2 + -12x2 = 0

Combine like terms: 12x2 + -12x2 = 0
39 + 13x + 0 = 0
39 + 13x = 0

Solving
39 + 13x = 0

Solving for variable 'x'.

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

Add '-39' to each side of the equation.
39 + -39 + 13x = 0 + -39

Combine like terms: 39 + -39 = 0
0 + 13x = 0 + -39
13x = 0 + -39

Combine like terms: 0 + -39 = -39
13x = -39

Divide each side by '13'.
x = -3

Simplifying
x = -3

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