H(x)=-3x^2+-12x

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Solution for H(x)=-3x^2+-12x equation: 


Simplifying
H(x) = -3x2 + -12x

Multiply H * x
xH = -3x2 + -12x

Reorder the terms:
xH = -12x + -3x2

Solving
xH = -12x + -3x2

Solving for variable 'x'.

Reorder the terms:
12x + xH + 3x2 = -12x + -3x2 + 12x + 3x2

Reorder the terms:
12x + xH + 3x2 = -12x + 12x + -3x2 + 3x2

Combine like terms: -12x + 12x = 0
12x + xH + 3x2 = 0 + -3x2 + 3x2
12x + xH + 3x2 = -3x2 + 3x2

Combine like terms: -3x2 + 3x2 = 0
12x + xH + 3x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(12 + H + 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 '(12 + H + 3x)' equal to zero and attempt to solve:

Simplifying
12 + H + 3x = 0

Solving
12 + H + 3x = 0

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

Add '-12' to each side of the equation.
12 + H + -12 + 3x = 0 + -12

Reorder the terms:
12 + -12 + H + 3x = 0 + -12

Combine like terms: 12 + -12 = 0
0 + H + 3x = 0 + -12
H + 3x = 0 + -12

Combine like terms: 0 + -12 = -12
H + 3x = -12

Add '-1H' to each side of the equation.
H + -1H + 3x = -12 + -1H

Combine like terms: H + -1H = 0
0 + 3x = -12 + -1H
3x = -12 + -1H

Divide each side by '3'.
x = -4 + -0.3333333333H

Simplifying
x = -4 + -0.3333333333H
Solution
x = {0, -4 + -0.3333333333H}

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