(2w-6)(5w+4)=-9w-21

Solution for (2w-6)(5w+4)=-9w-21 equation:

Simplifying
(2w + -6)(5w + 4) = -9w + -21

Reorder the terms:
(-6 + 2w)(5w + 4) = -9w + -21

Reorder the terms:
(-6 + 2w)(4 + 5w) = -9w + -21

Multiply (-6 + 2w) * (4 + 5w)
(-6(4 + 5w) + 2w * (4 + 5w)) = -9w + -21
((4 * -6 + 5w * -6) + 2w * (4 + 5w)) = -9w + -21
((-24 + -30w) + 2w * (4 + 5w)) = -9w + -21
(-24 + -30w + (4 * 2w + 5w * 2w)) = -9w + -21
(-24 + -30w + (8w + 10w2)) = -9w + -21

Combine like terms: -30w + 8w = -22w
(-24 + -22w + 10w2) = -9w + -21

Reorder the terms:
-24 + -22w + 10w2 = -21 + -9w

Solving
-24 + -22w + 10w2 = -21 + -9w

Solving for variable 'w'.

Reorder the terms:
-24 + 21 + -22w + 9w + 10w2 = -21 + -9w + 21 + 9w

Combine like terms: -24 + 21 = -3
-3 + -22w + 9w + 10w2 = -21 + -9w + 21 + 9w

Combine like terms: -22w + 9w = -13w
-3 + -13w + 10w2 = -21 + -9w + 21 + 9w

Reorder the terms:
-3 + -13w + 10w2 = -21 + 21 + -9w + 9w

Combine like terms: -21 + 21 = 0
-3 + -13w + 10w2 = 0 + -9w + 9w
-3 + -13w + 10w2 = -9w + 9w

Combine like terms: -9w + 9w = 0
-3 + -13w + 10w2 = 0

Factor a trinomial.
(-1 + -5w)(3 + -2w) = 0

Subproblem 1
Set the factor '(-1 + -5w)' equal to zero and attempt to solve:

Simplifying
-1 + -5w = 0

Solving
-1 + -5w = 0

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

Add '1' to each side of the equation.
-1 + 1 + -5w = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -5w = 0 + 1
-5w = 0 + 1

Combine like terms: 0 + 1 = 1
-5w = 1

Divide each side by '-5'.
w = -0.2

Simplifying
w = -0.2
Subproblem 2
Set the factor '(3 + -2w)' equal to zero and attempt to solve:

Simplifying
3 + -2w = 0

Solving
3 + -2w = 0

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

Add '-3' to each side of the equation.
3 + -3 + -2w = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2w = 0 + -3
-2w = 0 + -3

Combine like terms: 0 + -3 = -3
-2w = -3

Divide each side by '-2'.
w = 1.5

Simplifying
w = 1.5
Solution
w = {-0.2, 1.5}