H(x)=(2x+1)(4x-5)

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Solution for H(x)=(2x+1)(4x-5) equation: 


Simplifying
H(x) = (2x + 1)(4x + -5)

Multiply H * x
xH = (2x + 1)(4x + -5)

Reorder the terms:
xH = (1 + 2x)(4x + -5)

Reorder the terms:
xH = (1 + 2x)(-5 + 4x)

Multiply (1 + 2x) * (-5 + 4x)
xH = (1(-5 + 4x) + 2x * (-5 + 4x))
xH = ((-5 * 1 + 4x * 1) + 2x * (-5 + 4x))
xH = ((-5 + 4x) + 2x * (-5 + 4x))
xH = (-5 + 4x + (-5 * 2x + 4x * 2x))
xH = (-5 + 4x + (-10x + 8x2))

Combine like terms: 4x + -10x = -6x
xH = (-5 + -6x + 8x2)

Solving
xH = -5 + -6x + 8x2

Solving for variable 'x'.

Reorder the terms:
5 + 6x + xH + -8x2 = -5 + -6x + 8x2 + 5 + 6x + -8x2

Reorder the terms:
5 + 6x + xH + -8x2 = -5 + 5 + -6x + 6x + 8x2 + -8x2

Combine like terms: -5 + 5 = 0
5 + 6x + xH + -8x2 = 0 + -6x + 6x + 8x2 + -8x2
5 + 6x + xH + -8x2 = -6x + 6x + 8x2 + -8x2

Combine like terms: -6x + 6x = 0
5 + 6x + xH + -8x2 = 0 + 8x2 + -8x2
5 + 6x + xH + -8x2 = 8x2 + -8x2

Combine like terms: 8x2 + -8x2 = 0
5 + 6x + xH + -8x2 = 0

The solution to this equation could not be determined.

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