(2x-5)(2x-5)-(4x-10)(x+3)=0

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Solution for (2x-5)(2x-5)-(4x-10)(x+3)=0 equation: 


Simplifying
(2x + -5)(2x + -5) + -1(4x + -10)(x + 3) = 0

Reorder the terms:
(-5 + 2x)(2x + -5) + -1(4x + -10)(x + 3) = 0

Reorder the terms:
(-5 + 2x)(-5 + 2x) + -1(4x + -10)(x + 3) = 0

Multiply (-5 + 2x) * (-5 + 2x)
(-5(-5 + 2x) + 2x * (-5 + 2x)) + -1(4x + -10)(x + 3) = 0
((-5 * -5 + 2x * -5) + 2x * (-5 + 2x)) + -1(4x + -10)(x + 3) = 0
((25 + -10x) + 2x * (-5 + 2x)) + -1(4x + -10)(x + 3) = 0
(25 + -10x + (-5 * 2x + 2x * 2x)) + -1(4x + -10)(x + 3) = 0
(25 + -10x + (-10x + 4x2)) + -1(4x + -10)(x + 3) = 0

Combine like terms: -10x + -10x = -20x
(25 + -20x + 4x2) + -1(4x + -10)(x + 3) = 0

Reorder the terms:
25 + -20x + 4x2 + -1(-10 + 4x)(x + 3) = 0

Reorder the terms:
25 + -20x + 4x2 + -1(-10 + 4x)(3 + x) = 0

Multiply (-10 + 4x) * (3 + x)
25 + -20x + 4x2 + -1(-10(3 + x) + 4x * (3 + x)) = 0
25 + -20x + 4x2 + -1((3 * -10 + x * -10) + 4x * (3 + x)) = 0
25 + -20x + 4x2 + -1((-30 + -10x) + 4x * (3 + x)) = 0
25 + -20x + 4x2 + -1(-30 + -10x + (3 * 4x + x * 4x)) = 0
25 + -20x + 4x2 + -1(-30 + -10x + (12x + 4x2)) = 0

Combine like terms: -10x + 12x = 2x
25 + -20x + 4x2 + -1(-30 + 2x + 4x2) = 0
25 + -20x + 4x2 + (-30 * -1 + 2x * -1 + 4x2 * -1) = 0
25 + -20x + 4x2 + (30 + -2x + -4x2) = 0

Reorder the terms:
25 + 30 + -20x + -2x + 4x2 + -4x2 = 0

Combine like terms: 25 + 30 = 55
55 + -20x + -2x + 4x2 + -4x2 = 0

Combine like terms: -20x + -2x = -22x
55 + -22x + 4x2 + -4x2 = 0

Combine like terms: 4x2 + -4x2 = 0
55 + -22x + 0 = 0
55 + -22x = 0

Solving
55 + -22x = 0

Solving for variable 'x'.

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

Add '-55' to each side of the equation.
55 + -55 + -22x = 0 + -55

Combine like terms: 55 + -55 = 0
0 + -22x = 0 + -55
-22x = 0 + -55

Combine like terms: 0 + -55 = -55
-22x = -55

Divide each side by '-22'.
x = 2.5

Simplifying
x = 2.5

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