3h(h+2)+h=15-(h+4)

Solution for 3h(h+2)+h=15-(h+4) equation:

Simplifying
3h(h + 2) + h = 15 + -1(h + 4)

Reorder the terms:
3h(2 + h) + h = 15 + -1(h + 4)
(2 * 3h + h * 3h) + h = 15 + -1(h + 4)
(6h + 3h2) + h = 15 + -1(h + 4)

Reorder the terms:
6h + h + 3h2 = 15 + -1(h + 4)

Combine like terms: 6h + h = 7h
7h + 3h2 = 15 + -1(h + 4)

Reorder the terms:
7h + 3h2 = 15 + -1(4 + h)
7h + 3h2 = 15 + (4 * -1 + h * -1)
7h + 3h2 = 15 + (-4 + -1h)

Combine like terms: 15 + -4 = 11
7h + 3h2 = 11 + -1h

Solving
7h + 3h2 = 11 + -1h

Solving for variable 'h'.

Reorder the terms:
-11 + 7h + h + 3h2 = 11 + -1h + -11 + h

Combine like terms: 7h + h = 8h
-11 + 8h + 3h2 = 11 + -1h + -11 + h

Reorder the terms:
-11 + 8h + 3h2 = 11 + -11 + -1h + h

Combine like terms: 11 + -11 = 0
-11 + 8h + 3h2 = 0 + -1h + h
-11 + 8h + 3h2 = -1h + h

Combine like terms: -1h + h = 0
-11 + 8h + 3h2 = 0

Factor a trinomial.
(-11 + -3h)(1 + -1h) = 0

Subproblem 1
Set the factor '(-11 + -3h)' equal to zero and attempt to solve:

Simplifying
-11 + -3h = 0

Solving
-11 + -3h = 0

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

Add '11' to each side of the equation.
-11 + 11 + -3h = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -3h = 0 + 11
-3h = 0 + 11

Combine like terms: 0 + 11 = 11
-3h = 11

Divide each side by '-3'.
h = -3.666666667

Simplifying
h = -3.666666667
Subproblem 2
Set the factor '(1 + -1h)' equal to zero and attempt to solve:

Simplifying
1 + -1h = 0

Solving
1 + -1h = 0

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

Add '-1' to each side of the equation.
1 + -1 + -1h = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1h = 0 + -1
-1h = 0 + -1

Combine like terms: 0 + -1 = -1
-1h = -1

Divide each side by '-1'.
h = 1

Simplifying
h = 1
Solution
h = {-3.666666667, 1}