(37.5+10x)-(19.5x)=0.5(x-5)(x-15)

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Solution for (37.5+10x)-(19.5x)=0.5(x-5)(x-15) equation: 


Simplifying
(37.5 + 10x) + -1(19.5x) = 0.5(x + -5)(x + -15)

Remove parenthesis around (37.5 + 10x)
37.5 + 10x + -1(19.5x) = 0.5(x + -5)(x + -15)

Remove parenthesis around (19.5x)
37.5 + 10x + -1 * 19.5x = 0.5(x + -5)(x + -15)

Multiply -1 * 19.5
37.5 + 10x + -19.5x = 0.5(x + -5)(x + -15)

Combine like terms: 10x + -19.5x = -9.5x
37.5 + -9.5x = 0.5(x + -5)(x + -15)

Reorder the terms:
37.5 + -9.5x = 0.5(-5 + x)(x + -15)

Reorder the terms:
37.5 + -9.5x = 0.5(-5 + x)(-15 + x)

Multiply (-5 + x) * (-15 + x)
37.5 + -9.5x = 0.5(-5(-15 + x) + x(-15 + x))
37.5 + -9.5x = 0.5((-15 * -5 + x * -5) + x(-15 + x))
37.5 + -9.5x = 0.5((75 + -5x) + x(-15 + x))
37.5 + -9.5x = 0.5(75 + -5x + (-15 * x + x * x))
37.5 + -9.5x = 0.5(75 + -5x + (-15x + x2))

Combine like terms: -5x + -15x = -20x
37.5 + -9.5x = 0.5(75 + -20x + x2)
37.5 + -9.5x = (75 * 0.5 + -20x * 0.5 + x2 * 0.5)
37.5 + -9.5x = (37.5 + -10x + 0.5x2)

Add '-37.5' to each side of the equation.
37.5 + -37.5 + -9.5x = 37.5 + -10x + -37.5 + 0.5x2

Combine like terms: 37.5 + -37.5 = 0.0
0.0 + -9.5x = 37.5 + -10x + -37.5 + 0.5x2
-9.5x = 37.5 + -10x + -37.5 + 0.5x2

Reorder the terms:
-9.5x = 37.5 + -37.5 + -10x + 0.5x2

Combine like terms: 37.5 + -37.5 = 0.0
-9.5x = 0.0 + -10x + 0.5x2
-9.5x = -10x + 0.5x2

Solving
-9.5x = -10x + 0.5x2

Solving for variable 'x'.

Combine like terms: -9.5x + 10x = 0.5x
0.5x + -0.5x2 = -10x + 0.5x2 + 10x + -0.5x2

Reorder the terms:
0.5x + -0.5x2 = -10x + 10x + 0.5x2 + -0.5x2

Combine like terms: -10x + 10x = 0
0.5x + -0.5x2 = 0 + 0.5x2 + -0.5x2
0.5x + -0.5x2 = 0.5x2 + -0.5x2

Combine like terms: 0.5x2 + -0.5x2 = 0.0
0.5x + -0.5x2 = 0.0

The solution to this equation could not be determined.

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