H(4x)=3x^2-2x

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Solution for H(4x)=3x^2-2x equation: 


Simplifying
H(4x) = 3x2 + -2x

Remove parenthesis around (4x)
H * 4x = 3x2 + -2x

Reorder the terms for easier multiplication:
4H * x = 3x2 + -2x

Multiply H * x
4xH = 3x2 + -2x

Reorder the terms:
4xH = -2x + 3x2

Solving
4xH = -2x + 3x2

Solving for variable 'x'.

Reorder the terms:
2x + 4xH + -3x2 = -2x + 3x2 + 2x + -3x2

Reorder the terms:
2x + 4xH + -3x2 = -2x + 2x + 3x2 + -3x2

Combine like terms: -2x + 2x = 0
2x + 4xH + -3x2 = 0 + 3x2 + -3x2
2x + 4xH + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
2x + 4xH + -3x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(2 + 4H + -3x) = 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 '(2 + 4H + -3x)' equal to zero and attempt to solve:

Simplifying
2 + 4H + -3x = 0

Solving
2 + 4H + -3x = 0

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

Add '-2' to each side of the equation.
2 + 4H + -2 + -3x = 0 + -2

Reorder the terms:
2 + -2 + 4H + -3x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 4H + -3x = 0 + -2
4H + -3x = 0 + -2

Combine like terms: 0 + -2 = -2
4H + -3x = -2

Add '-4H' to each side of the equation.
4H + -4H + -3x = -2 + -4H

Combine like terms: 4H + -4H = 0
0 + -3x = -2 + -4H
-3x = -2 + -4H

Divide each side by '-3'.
x = 0.6666666667 + 1.333333333H

Simplifying
x = 0.6666666667 + 1.333333333H
Solution
x = {0, 0.6666666667 + 1.333333333H}

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