(x-3)*(2x-5)=(2x+1)*(x+4)

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Solution for (x-3)*(2x-5)=(2x+1)*(x+4) equation: 


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

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

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

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

Combine like terms: -6x + -5x = -11x
(15 + -11x + 2x2) = (2x + 1)(x + 4)

Reorder the terms:
15 + -11x + 2x2 = (1 + 2x)(x + 4)

Reorder the terms:
15 + -11x + 2x2 = (1 + 2x)(4 + x)

Multiply (1 + 2x) * (4 + x)
15 + -11x + 2x2 = (1(4 + x) + 2x * (4 + x))
15 + -11x + 2x2 = ((4 * 1 + x * 1) + 2x * (4 + x))
15 + -11x + 2x2 = ((4 + 1x) + 2x * (4 + x))
15 + -11x + 2x2 = (4 + 1x + (4 * 2x + x * 2x))
15 + -11x + 2x2 = (4 + 1x + (8x + 2x2))

Combine like terms: 1x + 8x = 9x
15 + -11x + 2x2 = (4 + 9x + 2x2)

Add '-2x2' to each side of the equation.
15 + -11x + 2x2 + -2x2 = 4 + 9x + 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
15 + -11x + 0 = 4 + 9x + 2x2 + -2x2
15 + -11x = 4 + 9x + 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
15 + -11x = 4 + 9x + 0
15 + -11x = 4 + 9x

Solving
15 + -11x = 4 + 9x

Solving for variable 'x'.

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

Add '-9x' to each side of the equation.
15 + -11x + -9x = 4 + 9x + -9x

Combine like terms: -11x + -9x = -20x
15 + -20x = 4 + 9x + -9x

Combine like terms: 9x + -9x = 0
15 + -20x = 4 + 0
15 + -20x = 4

Add '-15' to each side of the equation.
15 + -15 + -20x = 4 + -15

Combine like terms: 15 + -15 = 0
0 + -20x = 4 + -15
-20x = 4 + -15

Combine like terms: 4 + -15 = -11
-20x = -11

Divide each side by '-20'.
x = 0.55

Simplifying
x = 0.55

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