3h(67h-46)=78

Solution for 3h(67h-46)=78 equation:

Simplifying
3h(67h + -46) = 78

Reorder the terms:
3h(-46 + 67h) = 78
(-46 * 3h + 67h * 3h) = 78
(-138h + 201h2) = 78

Solving
-138h + 201h2 = 78

Solving for variable 'h'.

Reorder the terms:
-78 + -138h + 201h2 = 78 + -78

Combine like terms: 78 + -78 = 0
-78 + -138h + 201h2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-26 + -46h + 67h2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-26 + -46h + 67h2)' equal to zero and attempt to solve:

Simplifying
-26 + -46h + 67h2 = 0

Solving
-26 + -46h + 67h2 = 0

Begin completing the square.  Divide all terms by
67 the coefficient of the squared term: 

Divide each side by '67'.
-0.3880597015 + -0.6865671642h + h2 = 0

Move the constant term to the right:

Add '0.3880597015' to each side of the equation.
-0.3880597015 + -0.6865671642h + 0.3880597015 + h2 = 0 + 0.3880597015

Reorder the terms:
-0.3880597015 + 0.3880597015 + -0.6865671642h + h2 = 0 + 0.3880597015

Combine like terms: -0.3880597015 + 0.3880597015 = 0.0000000000
0.0000000000 + -0.6865671642h + h2 = 0 + 0.3880597015
-0.6865671642h + h2 = 0 + 0.3880597015

Combine like terms: 0 + 0.3880597015 = 0.3880597015
-0.6865671642h + h2 = 0.3880597015

The h term is -0.6865671642h.  Take half its coefficient (-0.3432835821).
Square it (0.1178436177) and add it to both sides.

Add '0.1178436177' to each side of the equation.
-0.6865671642h + 0.1178436177 + h2 = 0.3880597015 + 0.1178436177

Reorder the terms:
0.1178436177 + -0.6865671642h + h2 = 0.3880597015 + 0.1178436177

Combine like terms: 0.3880597015 + 0.1178436177 = 0.5059033192
0.1178436177 + -0.6865671642h + h2 = 0.5059033192

Factor a perfect square on the left side:
(h + -0.3432835821)(h + -0.3432835821) = 0.5059033192

Calculate the square root of the right side: 0.711268809

Break this problem into two subproblems by setting 
(h + -0.3432835821) equal to 0.711268809 and -0.711268809.

Subproblem 1
h + -0.3432835821 = 0.711268809

Simplifying
h + -0.3432835821 = 0.711268809

Reorder the terms:
-0.3432835821 + h = 0.711268809

Solving
-0.3432835821 + h = 0.711268809

Solving for variable 'h'.

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

Add '0.3432835821' to each side of the equation.
-0.3432835821 + 0.3432835821 + h = 0.711268809 + 0.3432835821

Combine like terms: -0.3432835821 + 0.3432835821 = 0.0000000000
0.0000000000 + h = 0.711268809 + 0.3432835821
h = 0.711268809 + 0.3432835821

Combine like terms: 0.711268809 + 0.3432835821 = 1.0545523911
h = 1.0545523911

Simplifying
h = 1.0545523911

Subproblem 2
h + -0.3432835821 = -0.711268809

Simplifying
h + -0.3432835821 = -0.711268809

Reorder the terms:
-0.3432835821 + h = -0.711268809

Solving
-0.3432835821 + h = -0.711268809

Solving for variable 'h'.

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

Add '0.3432835821' to each side of the equation.
-0.3432835821 + 0.3432835821 + h = -0.711268809 + 0.3432835821

Combine like terms: -0.3432835821 + 0.3432835821 = 0.0000000000
0.0000000000 + h = -0.711268809 + 0.3432835821
h = -0.711268809 + 0.3432835821

Combine like terms: -0.711268809 + 0.3432835821 = -0.3679852269
h = -0.3679852269

Simplifying
h = -0.3679852269

Solution
The solution to the problem is based on the solutions
from the subproblems.
h = {1.0545523911, -0.3679852269}
Solution
h = {1.0545523911, -0.3679852269}