7b^2-53b+28=0

Solution for 7b^2-53b+28=0 equation:

Simplifying
7b2 + -53b + 28 = 0

Reorder the terms:
28 + -53b + 7b2 = 0

Solving
28 + -53b + 7b2 = 0

Solving for variable 'b'.

Factor a trinomial.
(4 + -7b)(7 + -1b) = 0

Subproblem 1
Set the factor '(4 + -7b)' equal to zero and attempt to solve:

Simplifying
4 + -7b = 0

Solving
4 + -7b = 0

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

Add '-4' to each side of the equation.
4 + -4 + -7b = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -7b = 0 + -4
-7b = 0 + -4

Combine like terms: 0 + -4 = -4
-7b = -4

Divide each side by '-7'.
b = 0.5714285714

Simplifying
b = 0.5714285714
Subproblem 2
Set the factor '(7 + -1b)' equal to zero and attempt to solve:

Simplifying
7 + -1b = 0

Solving
7 + -1b = 0

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

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

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

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

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

Simplifying
b = 7
Solution
b = {0.5714285714, 7}