(h)(h)+(15)(15)=(2h+1)(2h+1)

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Solution for (h)(h)+(15)(15)=(2h+1)(2h+1) equation: 


Simplifying
(h)(h) + (15)(15) = (2h + 1)(2h + 1)

Multiply h * h
h2 + (15)(15) = (2h + 1)(2h + 1)

Multiply 15 * 15
h2 + 225 = (2h + 1)(2h + 1)

Reorder the terms:
225 + h2 = (2h + 1)(2h + 1)

Reorder the terms:
225 + h2 = (1 + 2h)(2h + 1)

Reorder the terms:
225 + h2 = (1 + 2h)(1 + 2h)

Multiply (1 + 2h) * (1 + 2h)
225 + h2 = (1(1 + 2h) + 2h * (1 + 2h))
225 + h2 = ((1 * 1 + 2h * 1) + 2h * (1 + 2h))
225 + h2 = ((1 + 2h) + 2h * (1 + 2h))
225 + h2 = (1 + 2h + (1 * 2h + 2h * 2h))
225 + h2 = (1 + 2h + (2h + 4h2))

Combine like terms: 2h + 2h = 4h
225 + h2 = (1 + 4h + 4h2)

Solving
225 + h2 = 1 + 4h + 4h2

Solving for variable 'h'.

Reorder the terms:
225 + -1 + -4h + h2 + -4h2 = 1 + 4h + 4h2 + -1 + -4h + -4h2

Combine like terms: 225 + -1 = 224
224 + -4h + h2 + -4h2 = 1 + 4h + 4h2 + -1 + -4h + -4h2

Combine like terms: h2 + -4h2 = -3h2
224 + -4h + -3h2 = 1 + 4h + 4h2 + -1 + -4h + -4h2

Reorder the terms:
224 + -4h + -3h2 = 1 + -1 + 4h + -4h + 4h2 + -4h2

Combine like terms: 1 + -1 = 0
224 + -4h + -3h2 = 0 + 4h + -4h + 4h2 + -4h2
224 + -4h + -3h2 = 4h + -4h + 4h2 + -4h2

Combine like terms: 4h + -4h = 0
224 + -4h + -3h2 = 0 + 4h2 + -4h2
224 + -4h + -3h2 = 4h2 + -4h2

Combine like terms: 4h2 + -4h2 = 0
224 + -4h + -3h2 = 0

Factor a trinomial.
(8 + -1h)(28 + 3h) = 0


Subproblem 1
Set the factor '(8 + -1h)' equal to zero and attempt to solve:

Simplifying
8 + -1h = 0

Solving
8 + -1h = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1h = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1h = 0 + -8
-1h = 0 + -8

Combine like terms: 0 + -8 = -8
-1h = -8

Divide each side by '-1'.
h = 8

Simplifying
h = 8

Subproblem 2
Set the factor '(28 + 3h)' equal to zero and attempt to solve:

Simplifying
28 + 3h = 0

Solving
28 + 3h = 0

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

Add '-28' to each side of the equation.
28 + -28 + 3h = 0 + -28

Combine like terms: 28 + -28 = 0
0 + 3h = 0 + -28
3h = 0 + -28

Combine like terms: 0 + -28 = -28
3h = -28

Divide each side by '3'.
h = -9.333333333

Simplifying
h = -9.333333333
Solution
h = {8, -9.333333333}

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