Simplifying
(2w + -5)(w + -3) = 55
Reorder the terms:
(-5 + 2w)(w + -3) = 55
Reorder the terms:
(-5 + 2w)(-3 + w) = 55
Multiply (-5 + 2w) * (-3 + w)
(-5(-3 + w) + 2w * (-3 + w)) = 55
((-3 * -5 + w * -5) + 2w * (-3 + w)) = 55
((15 + -5w) + 2w * (-3 + w)) = 55
(15 + -5w + (-3 * 2w + w * 2w)) = 55
(15 + -5w + (-6w + 2w2)) = 55
Combine like terms: -5w + -6w = -11w
(15 + -11w + 2w2) = 55
Solving
15 + -11w + 2w2 = 55
Solving for variable 'w'.
Reorder the terms:
15 + -55 + -11w + 2w2 = 55 + -55
Combine like terms: 15 + -55 = -40
-40 + -11w + 2w2 = 55 + -55
Combine like terms: 55 + -55 = 0
-40 + -11w + 2w2 = 0
Factor a trinomial.
(-5 + -2w)(8 + -1w) = 0
Subproblem 1
Set the factor '(-5 + -2w)' equal to zero and attempt to solve:
Simplifying
-5 + -2w = 0
Solving
-5 + -2w = 0
Move all terms containing w to the left, all other terms to the right.
Add '5' to each side of the equation.
-5 + 5 + -2w = 0 + 5
Combine like terms: -5 + 5 = 0
0 + -2w = 0 + 5
-2w = 0 + 5
Combine like terms: 0 + 5 = 5
-2w = 5
Divide each side by '-2'.
w = -2.5
Simplifying
w = -2.5
Subproblem 2
Set the factor '(8 + -1w)' equal to zero and attempt to solve:
Simplifying
8 + -1w = 0
Solving
8 + -1w = 0
Move all terms containing w to the left, all other terms to the right.
Add '-8' to each side of the equation.
8 + -8 + -1w = 0 + -8
Combine like terms: 8 + -8 = 0
0 + -1w = 0 + -8
-1w = 0 + -8
Combine like terms: 0 + -8 = -8
-1w = -8
Divide each side by '-1'.
w = 8
Simplifying
w = 8
Solution
w = {-2.5, 8}
