(2b+4)(b-3)=600

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Solution for (2b+4)(b-3)=600 equation: 


Simplifying
(2b + 4)(b + -3) = 600

Reorder the terms:
(4 + 2b)(b + -3) = 600

Reorder the terms:
(4 + 2b)(-3 + b) = 600

Multiply (4 + 2b) * (-3 + b)
(4(-3 + b) + 2b * (-3 + b)) = 600
((-3 * 4 + b * 4) + 2b * (-3 + b)) = 600
((-12 + 4b) + 2b * (-3 + b)) = 600
(-12 + 4b + (-3 * 2b + b * 2b)) = 600
(-12 + 4b + (-6b + 2b2)) = 600

Combine like terms: 4b + -6b = -2b
(-12 + -2b + 2b2) = 600

Solving
-12 + -2b + 2b2 = 600

Solving for variable 'b'.

Reorder the terms:
-12 + -600 + -2b + 2b2 = 600 + -600

Combine like terms: -12 + -600 = -612
-612 + -2b + 2b2 = 600 + -600

Combine like terms: 600 + -600 = 0
-612 + -2b + 2b2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-306 + -1b + b2) = 0

Factor a trinomial.
2((-17 + -1b)(18 + -1b)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-17 + -1b)' equal to zero and attempt to solve:

Simplifying
-17 + -1b = 0

Solving
-17 + -1b = 0

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

Add '17' to each side of the equation.
-17 + 17 + -1b = 0 + 17

Combine like terms: -17 + 17 = 0
0 + -1b = 0 + 17
-1b = 0 + 17

Combine like terms: 0 + 17 = 17
-1b = 17

Divide each side by '-1'.
b = -17

Simplifying
b = -17

Subproblem 2
Set the factor '(18 + -1b)' equal to zero and attempt to solve:

Simplifying
18 + -1b = 0

Solving
18 + -1b = 0

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

Add '-18' to each side of the equation.
18 + -18 + -1b = 0 + -18

Combine like terms: 18 + -18 = 0
0 + -1b = 0 + -18
-1b = 0 + -18

Combine like terms: 0 + -18 = -18
-1b = -18

Divide each side by '-1'.
b = 18

Simplifying
b = 18
Solution
b = {-17, 18}

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