72x^2=37x+5

Solution for 72x^2=37x+5 equation:

Simplifying
72x2 = 37x + 5

Reorder the terms:
72x2 = 5 + 37x

Solving
72x2 = 5 + 37x

Solving for variable 'x'.

Reorder the terms:
-5 + -37x + 72x2 = 5 + 37x + -5 + -37x

Reorder the terms:
-5 + -37x + 72x2 = 5 + -5 + 37x + -37x

Combine like terms: 5 + -5 = 0
-5 + -37x + 72x2 = 0 + 37x + -37x
-5 + -37x + 72x2 = 37x + -37x

Combine like terms: 37x + -37x = 0
-5 + -37x + 72x2 = 0

Factor a trinomial.
(-1 + -9x)(5 + -8x) = 0

Subproblem 1
Set the factor '(-1 + -9x)' equal to zero and attempt to solve:

Simplifying
-1 + -9x = 0

Solving
-1 + -9x = 0

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

Add '1' to each side of the equation.
-1 + 1 + -9x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -9x = 0 + 1
-9x = 0 + 1

Combine like terms: 0 + 1 = 1
-9x = 1

Divide each side by '-9'.
x = -0.1111111111

Simplifying
x = -0.1111111111
Subproblem 2
Set the factor '(5 + -8x)' equal to zero and attempt to solve:

Simplifying
5 + -8x = 0

Solving
5 + -8x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -8x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -8x = 0 + -5
-8x = 0 + -5

Combine like terms: 0 + -5 = -5
-8x = -5

Divide each side by '-8'.
x = 0.625

Simplifying
x = 0.625
Solution
x = {-0.1111111111, 0.625}