(x-4)(-2x+5)=0

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Solution for (x-4)(-2x+5)=0 equation:


Simplifying
(x + -4)(-2x + 5) = 0

Reorder the terms:
(-4 + x)(-2x + 5) = 0

Reorder the terms:
(-4 + x)(5 + -2x) = 0

Multiply (-4 + x) * (5 + -2x)
(-4(5 + -2x) + x(5 + -2x)) = 0
((5 * -4 + -2x * -4) + x(5 + -2x)) = 0
((-20 + 8x) + x(5 + -2x)) = 0
(-20 + 8x + (5 * x + -2x * x)) = 0
(-20 + 8x + (5x + -2x2)) = 0

Combine like terms: 8x + 5x = 13x
(-20 + 13x + -2x2) = 0

Solving
-20 + 13x + -2x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-4 + x)(5 + -2x) = 0

Subproblem 1

Set the factor '(-4 + x)' equal to zero and attempt to solve: Simplifying -4 + x = 0 Solving -4 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + x = 0 + 4 x = 0 + 4 Combine like terms: 0 + 4 = 4 x = 4 Simplifying x = 4

Subproblem 2

Set the factor '(5 + -2x)' equal to zero and attempt to solve: Simplifying 5 + -2x = 0 Solving 5 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -2x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2x = 0 + -5 -2x = 0 + -5 Combine like terms: 0 + -5 = -5 -2x = -5 Divide each side by '-2'. x = 2.5 Simplifying x = 2.5

Solution

x = {4, 2.5}

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