h^2+576=(2h+6)(2h+6)

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Solution for h^2+576=(2h+6)(2h+6) equation: 


Simplifying
h2 + 576 = (2h + 6)(2h + 6)

Reorder the terms:
576 + h2 = (2h + 6)(2h + 6)

Reorder the terms:
576 + h2 = (6 + 2h)(2h + 6)

Reorder the terms:
576 + h2 = (6 + 2h)(6 + 2h)

Multiply (6 + 2h) * (6 + 2h)
576 + h2 = (6(6 + 2h) + 2h * (6 + 2h))
576 + h2 = ((6 * 6 + 2h * 6) + 2h * (6 + 2h))
576 + h2 = ((36 + 12h) + 2h * (6 + 2h))
576 + h2 = (36 + 12h + (6 * 2h + 2h * 2h))
576 + h2 = (36 + 12h + (12h + 4h2))

Combine like terms: 12h + 12h = 24h
576 + h2 = (36 + 24h + 4h2)

Solving
576 + h2 = 36 + 24h + 4h2

Solving for variable 'h'.

Reorder the terms:
576 + -36 + -24h + h2 + -4h2 = 36 + 24h + 4h2 + -36 + -24h + -4h2

Combine like terms: 576 + -36 = 540
540 + -24h + h2 + -4h2 = 36 + 24h + 4h2 + -36 + -24h + -4h2

Combine like terms: h2 + -4h2 = -3h2
540 + -24h + -3h2 = 36 + 24h + 4h2 + -36 + -24h + -4h2

Reorder the terms:
540 + -24h + -3h2 = 36 + -36 + 24h + -24h + 4h2 + -4h2

Combine like terms: 36 + -36 = 0
540 + -24h + -3h2 = 0 + 24h + -24h + 4h2 + -4h2
540 + -24h + -3h2 = 24h + -24h + 4h2 + -4h2

Combine like terms: 24h + -24h = 0
540 + -24h + -3h2 = 0 + 4h2 + -4h2
540 + -24h + -3h2 = 4h2 + -4h2

Combine like terms: 4h2 + -4h2 = 0
540 + -24h + -3h2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(180 + -8h + -1h2) = 0

Factor a trinomial.
3((10 + -1h)(18 + h)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(10 + -1h)' equal to zero and attempt to solve:

Simplifying
10 + -1h = 0

Solving
10 + -1h = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1h = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1h = 0 + -10
-1h = 0 + -10

Combine like terms: 0 + -10 = -10
-1h = -10

Divide each side by '-1'.
h = 10

Simplifying
h = 10

Subproblem 2
Set the factor '(18 + h)' equal to zero and attempt to solve:

Simplifying
18 + h = 0

Solving
18 + h = 0

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

Add '-18' to each side of the equation.
18 + -18 + h = 0 + -18

Combine like terms: 18 + -18 = 0
0 + h = 0 + -18
h = 0 + -18

Combine like terms: 0 + -18 = -18
h = -18

Simplifying
h = -18
Solution
h = {10, -18}

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