(h+2)(h+5)=(h+1)(h+7)

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Solution for (h+2)(h+5)=(h+1)(h+7) equation: 


Simplifying
(h + 2)(h + 5) = (h + 1)(h + 7)

Reorder the terms:
(2 + h)(h + 5) = (h + 1)(h + 7)

Reorder the terms:
(2 + h)(5 + h) = (h + 1)(h + 7)

Multiply (2 + h) * (5 + h)
(2(5 + h) + h(5 + h)) = (h + 1)(h + 7)
((5 * 2 + h * 2) + h(5 + h)) = (h + 1)(h + 7)
((10 + 2h) + h(5 + h)) = (h + 1)(h + 7)
(10 + 2h + (5 * h + h * h)) = (h + 1)(h + 7)
(10 + 2h + (5h + h2)) = (h + 1)(h + 7)

Combine like terms: 2h + 5h = 7h
(10 + 7h + h2) = (h + 1)(h + 7)

Reorder the terms:
10 + 7h + h2 = (1 + h)(h + 7)

Reorder the terms:
10 + 7h + h2 = (1 + h)(7 + h)

Multiply (1 + h) * (7 + h)
10 + 7h + h2 = (1(7 + h) + h(7 + h))
10 + 7h + h2 = ((7 * 1 + h * 1) + h(7 + h))
10 + 7h + h2 = ((7 + 1h) + h(7 + h))
10 + 7h + h2 = (7 + 1h + (7 * h + h * h))
10 + 7h + h2 = (7 + 1h + (7h + h2))

Combine like terms: 1h + 7h = 8h
10 + 7h + h2 = (7 + 8h + h2)

Add '-1h2' to each side of the equation.
10 + 7h + h2 + -1h2 = 7 + 8h + h2 + -1h2

Combine like terms: h2 + -1h2 = 0
10 + 7h + 0 = 7 + 8h + h2 + -1h2
10 + 7h = 7 + 8h + h2 + -1h2

Combine like terms: h2 + -1h2 = 0
10 + 7h = 7 + 8h + 0
10 + 7h = 7 + 8h

Solving
10 + 7h = 7 + 8h

Solving for variable 'h'.

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

Add '-8h' to each side of the equation.
10 + 7h + -8h = 7 + 8h + -8h

Combine like terms: 7h + -8h = -1h
10 + -1h = 7 + 8h + -8h

Combine like terms: 8h + -8h = 0
10 + -1h = 7 + 0
10 + -1h = 7

Add '-10' to each side of the equation.
10 + -10 + -1h = 7 + -10

Combine like terms: 10 + -10 = 0
0 + -1h = 7 + -10
-1h = 7 + -10

Combine like terms: 7 + -10 = -3
-1h = -3

Divide each side by '-1'.
h = 3

Simplifying
h = 3

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