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

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


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

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

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

Multiply (-4 + 3x) * (-3 + 4x)
(-4(-3 + 4x) + 3x * (-3 + 4x)) = (6x + -4)(2x + -5)
((-3 * -4 + 4x * -4) + 3x * (-3 + 4x)) = (6x + -4)(2x + -5)
((12 + -16x) + 3x * (-3 + 4x)) = (6x + -4)(2x + -5)
(12 + -16x + (-3 * 3x + 4x * 3x)) = (6x + -4)(2x + -5)
(12 + -16x + (-9x + 12x2)) = (6x + -4)(2x + -5)

Combine like terms: -16x + -9x = -25x
(12 + -25x + 12x2) = (6x + -4)(2x + -5)

Reorder the terms:
12 + -25x + 12x2 = (-4 + 6x)(2x + -5)

Reorder the terms:
12 + -25x + 12x2 = (-4 + 6x)(-5 + 2x)

Multiply (-4 + 6x) * (-5 + 2x)
12 + -25x + 12x2 = (-4(-5 + 2x) + 6x * (-5 + 2x))
12 + -25x + 12x2 = ((-5 * -4 + 2x * -4) + 6x * (-5 + 2x))
12 + -25x + 12x2 = ((20 + -8x) + 6x * (-5 + 2x))
12 + -25x + 12x2 = (20 + -8x + (-5 * 6x + 2x * 6x))
12 + -25x + 12x2 = (20 + -8x + (-30x + 12x2))

Combine like terms: -8x + -30x = -38x
12 + -25x + 12x2 = (20 + -38x + 12x2)

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

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

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

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

Solving for variable 'x'.

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

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

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

Combine like terms: -38x + 38x = 0
12 + 13x = 20 + 0
12 + 13x = 20

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

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

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

Divide each side by '13'.
x = 0.6153846154

Simplifying
x = 0.6153846154

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