(x-5)(2x-3)+(7-2x)(x-5)=0

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Solution for (x-5)(2x-3)+(7-2x)(x-5)=0 equation: 


Simplifying
(x + -5)(2x + -3) + (7 + -2x)(x + -5) = 0

Reorder the terms:
(-5 + x)(2x + -3) + (7 + -2x)(x + -5) = 0

Reorder the terms:
(-5 + x)(-3 + 2x) + (7 + -2x)(x + -5) = 0

Multiply (-5 + x) * (-3 + 2x)
(-5(-3 + 2x) + x(-3 + 2x)) + (7 + -2x)(x + -5) = 0
((-3 * -5 + 2x * -5) + x(-3 + 2x)) + (7 + -2x)(x + -5) = 0
((15 + -10x) + x(-3 + 2x)) + (7 + -2x)(x + -5) = 0
(15 + -10x + (-3 * x + 2x * x)) + (7 + -2x)(x + -5) = 0
(15 + -10x + (-3x + 2x2)) + (7 + -2x)(x + -5) = 0

Combine like terms: -10x + -3x = -13x
(15 + -13x + 2x2) + (7 + -2x)(x + -5) = 0

Reorder the terms:
15 + -13x + 2x2 + (7 + -2x)(-5 + x) = 0

Multiply (7 + -2x) * (-5 + x)
15 + -13x + 2x2 + (7(-5 + x) + -2x * (-5 + x)) = 0
15 + -13x + 2x2 + ((-5 * 7 + x * 7) + -2x * (-5 + x)) = 0
15 + -13x + 2x2 + ((-35 + 7x) + -2x * (-5 + x)) = 0
15 + -13x + 2x2 + (-35 + 7x + (-5 * -2x + x * -2x)) = 0
15 + -13x + 2x2 + (-35 + 7x + (10x + -2x2)) = 0

Combine like terms: 7x + 10x = 17x
15 + -13x + 2x2 + (-35 + 17x + -2x2) = 0

Reorder the terms:
15 + -35 + -13x + 17x + 2x2 + -2x2 = 0

Combine like terms: 15 + -35 = -20
-20 + -13x + 17x + 2x2 + -2x2 = 0

Combine like terms: -13x + 17x = 4x
-20 + 4x + 2x2 + -2x2 = 0

Combine like terms: 2x2 + -2x2 = 0
-20 + 4x + 0 = 0
-20 + 4x = 0

Solving
-20 + 4x = 0

Solving for variable 'x'.

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

Add '20' to each side of the equation.
-20 + 20 + 4x = 0 + 20

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

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

Divide each side by '4'.
x = 5

Simplifying
x = 5

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