(2x-5)(6x-4)=(4x-3)(3x-4)

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Solution for (2x-5)(6x-4)=(4x-3)(3x-4) equation: 


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

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

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

Multiply (-5 + 2x) * (-4 + 6x)
(-5(-4 + 6x) + 2x * (-4 + 6x)) = (4x + -3)(3x + -4)
((-4 * -5 + 6x * -5) + 2x * (-4 + 6x)) = (4x + -3)(3x + -4)
((20 + -30x) + 2x * (-4 + 6x)) = (4x + -3)(3x + -4)
(20 + -30x + (-4 * 2x + 6x * 2x)) = (4x + -3)(3x + -4)
(20 + -30x + (-8x + 12x2)) = (4x + -3)(3x + -4)

Combine like terms: -30x + -8x = -38x
(20 + -38x + 12x2) = (4x + -3)(3x + -4)

Reorder the terms:
20 + -38x + 12x2 = (-3 + 4x)(3x + -4)

Reorder the terms:
20 + -38x + 12x2 = (-3 + 4x)(-4 + 3x)

Multiply (-3 + 4x) * (-4 + 3x)
20 + -38x + 12x2 = (-3(-4 + 3x) + 4x * (-4 + 3x))
20 + -38x + 12x2 = ((-4 * -3 + 3x * -3) + 4x * (-4 + 3x))
20 + -38x + 12x2 = ((12 + -9x) + 4x * (-4 + 3x))
20 + -38x + 12x2 = (12 + -9x + (-4 * 4x + 3x * 4x))
20 + -38x + 12x2 = (12 + -9x + (-16x + 12x2))

Combine like terms: -9x + -16x = -25x
20 + -38x + 12x2 = (12 + -25x + 12x2)

Add '-12x2' to each side of the equation.
20 + -38x + 12x2 + -12x2 = 12 + -25x + 12x2 + -12x2

Combine like terms: 12x2 + -12x2 = 0
20 + -38x + 0 = 12 + -25x + 12x2 + -12x2
20 + -38x = 12 + -25x + 12x2 + -12x2

Combine like terms: 12x2 + -12x2 = 0
20 + -38x = 12 + -25x + 0
20 + -38x = 12 + -25x

Solving
20 + -38x = 12 + -25x

Solving for variable 'x'.

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

Add '25x' to each side of the equation.
20 + -38x + 25x = 12 + -25x + 25x

Combine like terms: -38x + 25x = -13x
20 + -13x = 12 + -25x + 25x

Combine like terms: -25x + 25x = 0
20 + -13x = 12 + 0
20 + -13x = 12

Add '-20' to each side of the equation.
20 + -20 + -13x = 12 + -20

Combine like terms: 20 + -20 = 0
0 + -13x = 12 + -20
-13x = 12 + -20

Combine like terms: 12 + -20 = -8
-13x = -8

Divide each side by '-13'.
x = 0.6153846154

Simplifying
x = 0.6153846154

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