h^2+576=(3h+4)(3h+4)

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Solution for h^2+576=(3h+4)(3h+4) equation: 


Simplifying
h2 + 576 = (3h + 4)(3h + 4)

Reorder the terms:
576 + h2 = (3h + 4)(3h + 4)

Reorder the terms:
576 + h2 = (4 + 3h)(3h + 4)

Reorder the terms:
576 + h2 = (4 + 3h)(4 + 3h)

Multiply (4 + 3h) * (4 + 3h)
576 + h2 = (4(4 + 3h) + 3h * (4 + 3h))
576 + h2 = ((4 * 4 + 3h * 4) + 3h * (4 + 3h))
576 + h2 = ((16 + 12h) + 3h * (4 + 3h))
576 + h2 = (16 + 12h + (4 * 3h + 3h * 3h))
576 + h2 = (16 + 12h + (12h + 9h2))

Combine like terms: 12h + 12h = 24h
576 + h2 = (16 + 24h + 9h2)

Solving
576 + h2 = 16 + 24h + 9h2

Solving for variable 'h'.

Reorder the terms:
576 + -16 + -24h + h2 + -9h2 = 16 + 24h + 9h2 + -16 + -24h + -9h2

Combine like terms: 576 + -16 = 560
560 + -24h + h2 + -9h2 = 16 + 24h + 9h2 + -16 + -24h + -9h2

Combine like terms: h2 + -9h2 = -8h2
560 + -24h + -8h2 = 16 + 24h + 9h2 + -16 + -24h + -9h2

Reorder the terms:
560 + -24h + -8h2 = 16 + -16 + 24h + -24h + 9h2 + -9h2

Combine like terms: 16 + -16 = 0
560 + -24h + -8h2 = 0 + 24h + -24h + 9h2 + -9h2
560 + -24h + -8h2 = 24h + -24h + 9h2 + -9h2

Combine like terms: 24h + -24h = 0
560 + -24h + -8h2 = 0 + 9h2 + -9h2
560 + -24h + -8h2 = 9h2 + -9h2

Combine like terms: 9h2 + -9h2 = 0
560 + -24h + -8h2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(70 + -3h + -1h2) = 0

Factor a trinomial.
8((7 + -1h)(10 + h)) = 0

Ignore the factor 8.

Subproblem 1
Set the factor '(7 + -1h)' equal to zero and attempt to solve:

Simplifying
7 + -1h = 0

Solving
7 + -1h = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1h = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1h = 0 + -7
-1h = 0 + -7

Combine like terms: 0 + -7 = -7
-1h = -7

Divide each side by '-1'.
h = 7

Simplifying
h = 7

Subproblem 2
Set the factor '(10 + h)' equal to zero and attempt to solve:

Simplifying
10 + h = 0

Solving
10 + h = 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 + h = 0 + -10

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

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

Simplifying
h = -10
Solution
h = {7, -10}

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