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

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


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

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

Multiply (-5 + 2x) * (4 + -3x)
(-5(4 + -3x) + 2x * (4 + -3x)) = -6x(x + -2)
((4 * -5 + -3x * -5) + 2x * (4 + -3x)) = -6x(x + -2)
((-20 + 15x) + 2x * (4 + -3x)) = -6x(x + -2)
(-20 + 15x + (4 * 2x + -3x * 2x)) = -6x(x + -2)
(-20 + 15x + (8x + -6x2)) = -6x(x + -2)

Combine like terms: 15x + 8x = 23x
(-20 + 23x + -6x2) = -6x(x + -2)

Reorder the terms:
-20 + 23x + -6x2 = -6x(-2 + x)
-20 + 23x + -6x2 = (-2 * -6x + x * -6x)
-20 + 23x + -6x2 = (12x + -6x2)

Add '6x2' to each side of the equation.
-20 + 23x + -6x2 + 6x2 = 12x + -6x2 + 6x2

Combine like terms: -6x2 + 6x2 = 0
-20 + 23x + 0 = 12x + -6x2 + 6x2
-20 + 23x = 12x + -6x2 + 6x2

Combine like terms: -6x2 + 6x2 = 0
-20 + 23x = 12x + 0
-20 + 23x = 12x

Solving
-20 + 23x = 12x

Solving for variable 'x'.

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

Add '-12x' to each side of the equation.
-20 + 23x + -12x = 12x + -12x

Combine like terms: 23x + -12x = 11x
-20 + 11x = 12x + -12x

Combine like terms: 12x + -12x = 0
-20 + 11x = 0

Add '20' to each side of the equation.
-20 + 20 + 11x = 0 + 20

Combine like terms: -20 + 20 = 0
0 + 11x = 0 + 20
11x = 0 + 20

Combine like terms: 0 + 20 = 20
11x = 20

Divide each side by '11'.
x = 1.818181818

Simplifying
x = 1.818181818

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