(4w-3)(5w+4)=2w-11

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Solution for (4w-3)(5w+4)=2w-11 equation:


Simplifying
(4w + -3)(5w + 4) = 2w + -11

Reorder the terms:
(-3 + 4w)(5w + 4) = 2w + -11

Reorder the terms:
(-3 + 4w)(4 + 5w) = 2w + -11

Multiply (-3 + 4w) * (4 + 5w)
(-3(4 + 5w) + 4w * (4 + 5w)) = 2w + -11
((4 * -3 + 5w * -3) + 4w * (4 + 5w)) = 2w + -11
((-12 + -15w) + 4w * (4 + 5w)) = 2w + -11
(-12 + -15w + (4 * 4w + 5w * 4w)) = 2w + -11
(-12 + -15w + (16w + 20w2)) = 2w + -11

Combine like terms: -15w + 16w = 1w
(-12 + 1w + 20w2) = 2w + -11

Reorder the terms:
-12 + 1w + 20w2 = -11 + 2w

Solving
-12 + 1w + 20w2 = -11 + 2w

Solving for variable 'w'.

Reorder the terms:
-12 + 11 + 1w + -2w + 20w2 = -11 + 2w + 11 + -2w

Combine like terms: -12 + 11 = -1
-1 + 1w + -2w + 20w2 = -11 + 2w + 11 + -2w

Combine like terms: 1w + -2w = -1w
-1 + -1w + 20w2 = -11 + 2w + 11 + -2w

Reorder the terms:
-1 + -1w + 20w2 = -11 + 11 + 2w + -2w

Combine like terms: -11 + 11 = 0
-1 + -1w + 20w2 = 0 + 2w + -2w
-1 + -1w + 20w2 = 2w + -2w

Combine like terms: 2w + -2w = 0
-1 + -1w + 20w2 = 0

Factor a trinomial.
(-1 + -5w)(1 + -4w) = 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 '(1 + -4w)' equal to zero and attempt to solve: Simplifying 1 + -4w = 0 Solving 1 + -4w = 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 + -4w = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4w = 0 + -1 -4w = 0 + -1 Combine like terms: 0 + -1 = -1 -4w = -1 Divide each side by '-4'. w = 0.25 Simplifying w = 0.25

Solution

w = {-0.2, 0.25}

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