(2x-6)(2x-5)=(4x+1)(x-4)

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


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

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

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

Multiply (-6 + 2x) * (-5 + 2x)
(-6(-5 + 2x) + 2x * (-5 + 2x)) = (4x + 1)(x + -4)
((-5 * -6 + 2x * -6) + 2x * (-5 + 2x)) = (4x + 1)(x + -4)
((30 + -12x) + 2x * (-5 + 2x)) = (4x + 1)(x + -4)
(30 + -12x + (-5 * 2x + 2x * 2x)) = (4x + 1)(x + -4)
(30 + -12x + (-10x + 4x2)) = (4x + 1)(x + -4)

Combine like terms: -12x + -10x = -22x
(30 + -22x + 4x2) = (4x + 1)(x + -4)

Reorder the terms:
30 + -22x + 4x2 = (1 + 4x)(x + -4)

Reorder the terms:
30 + -22x + 4x2 = (1 + 4x)(-4 + x)

Multiply (1 + 4x) * (-4 + x)
30 + -22x + 4x2 = (1(-4 + x) + 4x * (-4 + x))
30 + -22x + 4x2 = ((-4 * 1 + x * 1) + 4x * (-4 + x))
30 + -22x + 4x2 = ((-4 + 1x) + 4x * (-4 + x))
30 + -22x + 4x2 = (-4 + 1x + (-4 * 4x + x * 4x))
30 + -22x + 4x2 = (-4 + 1x + (-16x + 4x2))

Combine like terms: 1x + -16x = -15x
30 + -22x + 4x2 = (-4 + -15x + 4x2)

Add '-4x2' to each side of the equation.
30 + -22x + 4x2 + -4x2 = -4 + -15x + 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
30 + -22x + 0 = -4 + -15x + 4x2 + -4x2
30 + -22x = -4 + -15x + 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
30 + -22x = -4 + -15x + 0
30 + -22x = -4 + -15x

Solving
30 + -22x = -4 + -15x

Solving for variable 'x'.

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

Add '15x' to each side of the equation.
30 + -22x + 15x = -4 + -15x + 15x

Combine like terms: -22x + 15x = -7x
30 + -7x = -4 + -15x + 15x

Combine like terms: -15x + 15x = 0
30 + -7x = -4 + 0
30 + -7x = -4

Add '-30' to each side of the equation.
30 + -30 + -7x = -4 + -30

Combine like terms: 30 + -30 = 0
0 + -7x = -4 + -30
-7x = -4 + -30

Combine like terms: -4 + -30 = -34
-7x = -34

Divide each side by '-7'.
x = 4.857142857

Simplifying
x = 4.857142857

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