(2x+3)(3x+-2.5)=(6x-1)(x-2)

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Solution for (2x+3)(3x+-2.5)=(6x-1)(x-2) equation: 


Simplifying
(2x + 3)(3x + -2.5) = (6x + -1)(x + -2)

Reorder the terms:
(3 + 2x)(3x + -2.5) = (6x + -1)(x + -2)

Reorder the terms:
(3 + 2x)(-2.5 + 3x) = (6x + -1)(x + -2)

Multiply (3 + 2x) * (-2.5 + 3x)
(3(-2.5 + 3x) + 2x * (-2.5 + 3x)) = (6x + -1)(x + -2)
((-2.5 * 3 + 3x * 3) + 2x * (-2.5 + 3x)) = (6x + -1)(x + -2)
((-7.5 + 9x) + 2x * (-2.5 + 3x)) = (6x + -1)(x + -2)
(-7.5 + 9x + (-2.5 * 2x + 3x * 2x)) = (6x + -1)(x + -2)
(-7.5 + 9x + (-5x + 6x2)) = (6x + -1)(x + -2)

Combine like terms: 9x + -5x = 4x
(-7.5 + 4x + 6x2) = (6x + -1)(x + -2)

Reorder the terms:
-7.5 + 4x + 6x2 = (-1 + 6x)(x + -2)

Reorder the terms:
-7.5 + 4x + 6x2 = (-1 + 6x)(-2 + x)

Multiply (-1 + 6x) * (-2 + x)
-7.5 + 4x + 6x2 = (-1(-2 + x) + 6x * (-2 + x))
-7.5 + 4x + 6x2 = ((-2 * -1 + x * -1) + 6x * (-2 + x))
-7.5 + 4x + 6x2 = ((2 + -1x) + 6x * (-2 + x))
-7.5 + 4x + 6x2 = (2 + -1x + (-2 * 6x + x * 6x))
-7.5 + 4x + 6x2 = (2 + -1x + (-12x + 6x2))

Combine like terms: -1x + -12x = -13x
-7.5 + 4x + 6x2 = (2 + -13x + 6x2)

Add '-6x2' to each side of the equation.
-7.5 + 4x + 6x2 + -6x2 = 2 + -13x + 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
-7.5 + 4x + 0 = 2 + -13x + 6x2 + -6x2
-7.5 + 4x = 2 + -13x + 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
-7.5 + 4x = 2 + -13x + 0
-7.5 + 4x = 2 + -13x

Solving
-7.5 + 4x = 2 + -13x

Solving for variable 'x'.

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

Add '13x' to each side of the equation.
-7.5 + 4x + 13x = 2 + -13x + 13x

Combine like terms: 4x + 13x = 17x
-7.5 + 17x = 2 + -13x + 13x

Combine like terms: -13x + 13x = 0
-7.5 + 17x = 2 + 0
-7.5 + 17x = 2

Add '7.5' to each side of the equation.
-7.5 + 7.5 + 17x = 2 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + 17x = 2 + 7.5
17x = 2 + 7.5

Combine like terms: 2 + 7.5 = 9.5
17x = 9.5

Divide each side by '17'.
x = 0.5588235294

Simplifying
x = 0.5588235294

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