H(x)=(5x+8)(2x+4x)

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Solution for H(x)=(5x+8)(2x+4x) equation: 


Simplifying
H(x) = (5x + 8)(2x + 4x)

Multiply H * x
xH = (5x + 8)(2x + 4x)

Reorder the terms:
xH = (8 + 5x)(2x + 4x)

Combine like terms: 2x + 4x = 6x
xH = (8 + 5x)(6x)

Remove parenthesis around (6x)
xH = (8 + 5x) * 6x

Reorder the terms for easier multiplication:
xH = 6x(8 + 5x)
xH = (8 * 6x + 5x * 6x)
xH = (48x + 30x2)

Solving
xH = 48x + 30x2

Solving for variable 'x'.

Reorder the terms:
-48x + xH + -30x2 = 48x + 30x2 + -48x + -30x2

Reorder the terms:
-48x + xH + -30x2 = 48x + -48x + 30x2 + -30x2

Combine like terms: 48x + -48x = 0
-48x + xH + -30x2 = 0 + 30x2 + -30x2
-48x + xH + -30x2 = 30x2 + -30x2

Combine like terms: 30x2 + -30x2 = 0
-48x + xH + -30x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-48 + H + -30x) = 0


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(-48 + H + -30x)' equal to zero and attempt to solve:

Simplifying
-48 + H + -30x = 0

Solving
-48 + H + -30x = 0

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

Add '48' to each side of the equation.
-48 + H + 48 + -30x = 0 + 48

Reorder the terms:
-48 + 48 + H + -30x = 0 + 48

Combine like terms: -48 + 48 = 0
0 + H + -30x = 0 + 48
H + -30x = 0 + 48

Combine like terms: 0 + 48 = 48
H + -30x = 48

Add '-1H' to each side of the equation.
H + -1H + -30x = 48 + -1H

Combine like terms: H + -1H = 0
0 + -30x = 48 + -1H
-30x = 48 + -1H

Divide each side by '-30'.
x = -1.6 + 0.03333333333H

Simplifying
x = -1.6 + 0.03333333333H
Solution
x = {0, -1.6 + 0.03333333333H}

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