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

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


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

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

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

Reorder the terms:
10 + -7x + 1x2 + -1x(-3 + x) = 0
10 + -7x + 1x2 + (-3 * -1x + x * -1x) = 0
10 + -7x + 1x2 + (3x + -1x2) = 0

Reorder the terms:
10 + -7x + 3x + 1x2 + -1x2 = 0

Combine like terms: -7x + 3x = -4x
10 + -4x + 1x2 + -1x2 = 0

Combine like terms: 1x2 + -1x2 = 0
10 + -4x + 0 = 0
10 + -4x = 0

Solving
10 + -4x = 0

Solving for variable 'x'.

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

Add '-10' to each side of the equation.
10 + -10 + -4x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -4x = 0 + -10
-4x = 0 + -10

Combine like terms: 0 + -10 = -10
-4x = -10

Divide each side by '-4'.
x = 2.5

Simplifying
x = 2.5

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