(-7b+2b-3)(5b-2b+4)=0

Solution for (-7b+2b-3)(5b-2b+4)=0 equation:

Simplifying
(-7b + 2b + -3)(5b + -2b + 4) = 0

Reorder the terms:
(-3 + -7b + 2b)(5b + -2b + 4) = 0

Combine like terms: -7b + 2b = -5b
(-3 + -5b)(5b + -2b + 4) = 0

Reorder the terms:
(-3 + -5b)(4 + 5b + -2b) = 0

Combine like terms: 5b + -2b = 3b
(-3 + -5b)(4 + 3b) = 0

Multiply (-3 + -5b) * (4 + 3b)
(-3(4 + 3b) + -5b * (4 + 3b)) = 0
((4 * -3 + 3b * -3) + -5b * (4 + 3b)) = 0
((-12 + -9b) + -5b * (4 + 3b)) = 0
(-12 + -9b + (4 * -5b + 3b * -5b)) = 0
(-12 + -9b + (-20b + -15b2)) = 0

Combine like terms: -9b + -20b = -29b
(-12 + -29b + -15b2) = 0

Solving
-12 + -29b + -15b2 = 0

Solving for variable 'b'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(12 + 29b + 15b2) = 0

Factor a trinomial.
-1((4 + 3b)(3 + 5b)) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(4 + 3b)' equal to zero and attempt to solve:

Simplifying
4 + 3b = 0

Solving
4 + 3b = 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 + 3b = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 3b = 0 + -4
3b = 0 + -4

Combine like terms: 0 + -4 = -4
3b = -4

Divide each side by '3'.
b = -1.333333333

Simplifying
b = -1.333333333
Subproblem 2
Set the factor '(3 + 5b)' equal to zero and attempt to solve:

Simplifying
3 + 5b = 0

Solving
3 + 5b = 0

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

Add '-3' to each side of the equation.
3 + -3 + 5b = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 5b = 0 + -3
5b = 0 + -3

Combine like terms: 0 + -3 = -3
5b = -3

Divide each side by '5'.
b = -0.6

Simplifying
b = -0.6
Solution
b = {-1.333333333, -0.6}