(4w-7)(5w-3)=-36w+24

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Solution for (4w-7)(5w-3)=-36w+24 equation:


Simplifying
(4w + -7)(5w + -3) = -36w + 24

Reorder the terms:
(-7 + 4w)(5w + -3) = -36w + 24

Reorder the terms:
(-7 + 4w)(-3 + 5w) = -36w + 24

Multiply (-7 + 4w) * (-3 + 5w)
(-7(-3 + 5w) + 4w * (-3 + 5w)) = -36w + 24
((-3 * -7 + 5w * -7) + 4w * (-3 + 5w)) = -36w + 24
((21 + -35w) + 4w * (-3 + 5w)) = -36w + 24
(21 + -35w + (-3 * 4w + 5w * 4w)) = -36w + 24
(21 + -35w + (-12w + 20w2)) = -36w + 24

Combine like terms: -35w + -12w = -47w
(21 + -47w + 20w2) = -36w + 24

Reorder the terms:
21 + -47w + 20w2 = 24 + -36w

Solving
21 + -47w + 20w2 = 24 + -36w

Solving for variable 'w'.

Reorder the terms:
21 + -24 + -47w + 36w + 20w2 = 24 + -36w + -24 + 36w

Combine like terms: 21 + -24 = -3
-3 + -47w + 36w + 20w2 = 24 + -36w + -24 + 36w

Combine like terms: -47w + 36w = -11w
-3 + -11w + 20w2 = 24 + -36w + -24 + 36w

Reorder the terms:
-3 + -11w + 20w2 = 24 + -24 + -36w + 36w

Combine like terms: 24 + -24 = 0
-3 + -11w + 20w2 = 0 + -36w + 36w
-3 + -11w + 20w2 = -36w + 36w

Combine like terms: -36w + 36w = 0
-3 + -11w + 20w2 = 0

Factor a trinomial.
(-1 + -5w)(3 + -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 '(3 + -4w)' equal to zero and attempt to solve: Simplifying 3 + -4w = 0 Solving 3 + -4w = 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 + -4w = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4w = 0 + -3 -4w = 0 + -3 Combine like terms: 0 + -3 = -3 -4w = -3 Divide each side by '-4'. w = 0.75 Simplifying w = 0.75

Solution

w = {-0.2, 0.75}

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