(2x-3)(x+5)-(3-x)(5-2x)=0

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Solution for (2x-3)(x+5)-(3-x)(5-2x)=0 equation: 


Simplifying
(2x + -3)(x + 5) + -1(3 + -1x)(5 + -2x) = 0

Reorder the terms:
(-3 + 2x)(x + 5) + -1(3 + -1x)(5 + -2x) = 0

Reorder the terms:
(-3 + 2x)(5 + x) + -1(3 + -1x)(5 + -2x) = 0

Multiply (-3 + 2x) * (5 + x)
(-3(5 + x) + 2x * (5 + x)) + -1(3 + -1x)(5 + -2x) = 0
((5 * -3 + x * -3) + 2x * (5 + x)) + -1(3 + -1x)(5 + -2x) = 0
((-15 + -3x) + 2x * (5 + x)) + -1(3 + -1x)(5 + -2x) = 0
(-15 + -3x + (5 * 2x + x * 2x)) + -1(3 + -1x)(5 + -2x) = 0
(-15 + -3x + (10x + 2x2)) + -1(3 + -1x)(5 + -2x) = 0

Combine like terms: -3x + 10x = 7x
(-15 + 7x + 2x2) + -1(3 + -1x)(5 + -2x) = 0

Multiply (3 + -1x) * (5 + -2x)
-15 + 7x + 2x2 + -1(3(5 + -2x) + -1x * (5 + -2x)) = 0
-15 + 7x + 2x2 + -1((5 * 3 + -2x * 3) + -1x * (5 + -2x)) = 0
-15 + 7x + 2x2 + -1((15 + -6x) + -1x * (5 + -2x)) = 0
-15 + 7x + 2x2 + -1(15 + -6x + (5 * -1x + -2x * -1x)) = 0
-15 + 7x + 2x2 + -1(15 + -6x + (-5x + 2x2)) = 0

Combine like terms: -6x + -5x = -11x
-15 + 7x + 2x2 + -1(15 + -11x + 2x2) = 0
-15 + 7x + 2x2 + (15 * -1 + -11x * -1 + 2x2 * -1) = 0
-15 + 7x + 2x2 + (-15 + 11x + -2x2) = 0

Reorder the terms:
-15 + -15 + 7x + 11x + 2x2 + -2x2 = 0

Combine like terms: -15 + -15 = -30
-30 + 7x + 11x + 2x2 + -2x2 = 0

Combine like terms: 7x + 11x = 18x
-30 + 18x + 2x2 + -2x2 = 0

Combine like terms: 2x2 + -2x2 = 0
-30 + 18x + 0 = 0
-30 + 18x = 0

Solving
-30 + 18x = 0

Solving for variable 'x'.

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

Add '30' to each side of the equation.
-30 + 30 + 18x = 0 + 30

Combine like terms: -30 + 30 = 0
0 + 18x = 0 + 30
18x = 0 + 30

Combine like terms: 0 + 30 = 30
18x = 30

Divide each side by '18'.
x = 1.666666667

Simplifying
x = 1.666666667

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