5h-7=5h(h-2)+3

Solution for 5h-7=5h(h-2)+3 equation:

Simplifying
5h + -7 = 5h(h + -2) + 3

Reorder the terms:
-7 + 5h = 5h(h + -2) + 3

Reorder the terms:
-7 + 5h = 5h(-2 + h) + 3
-7 + 5h = (-2 * 5h + h * 5h) + 3
-7 + 5h = (-10h + 5h2) + 3

Reorder the terms:
-7 + 5h = 3 + -10h + 5h2

Solving
-7 + 5h = 3 + -10h + 5h2

Solving for variable 'h'.

Reorder the terms:
-7 + -3 + 5h + 10h + -5h2 = 3 + -10h + 5h2 + -3 + 10h + -5h2

Combine like terms: -7 + -3 = -10
-10 + 5h + 10h + -5h2 = 3 + -10h + 5h2 + -3 + 10h + -5h2

Combine like terms: 5h + 10h = 15h
-10 + 15h + -5h2 = 3 + -10h + 5h2 + -3 + 10h + -5h2

Reorder the terms:
-10 + 15h + -5h2 = 3 + -3 + -10h + 10h + 5h2 + -5h2

Combine like terms: 3 + -3 = 0
-10 + 15h + -5h2 = 0 + -10h + 10h + 5h2 + -5h2
-10 + 15h + -5h2 = -10h + 10h + 5h2 + -5h2

Combine like terms: -10h + 10h = 0
-10 + 15h + -5h2 = 0 + 5h2 + -5h2
-10 + 15h + -5h2 = 5h2 + -5h2

Combine like terms: 5h2 + -5h2 = 0
-10 + 15h + -5h2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-2 + 3h + -1h2) = 0

Factor a trinomial.
5((-2 + h)(1 + -1h)) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(-2 + h)' equal to zero and attempt to solve:

Simplifying
-2 + h = 0

Solving
-2 + h = 0

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

Add '2' to each side of the equation.
-2 + 2 + h = 0 + 2

Combine like terms: -2 + 2 = 0
0 + h = 0 + 2
h = 0 + 2

Combine like terms: 0 + 2 = 2
h = 2

Simplifying
h = 2
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 = {2, 1}