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

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


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

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

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

Multiply (-5 + x) * (-5 + 4x)
(-5(-5 + 4x) + x(-5 + 4x)) = 0
((-5 * -5 + 4x * -5) + x(-5 + 4x)) = 0
((25 + -20x) + x(-5 + 4x)) = 0
(25 + -20x + (-5 * x + 4x * x)) = 0
(25 + -20x + (-5x + 4x2)) = 0

Combine like terms: -20x + -5x = -25x
(25 + -25x + 4x2) = 0

Solving
25 + -25x + 4x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(5 + -4x)(5 + -1x) = 0

Subproblem 1

Set the factor '(5 + -4x)' equal to zero and attempt to solve: Simplifying 5 + -4x = 0 Solving 5 + -4x = 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 + -4x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -4x = 0 + -5 -4x = 0 + -5 Combine like terms: 0 + -5 = -5 -4x = -5 Divide each side by '-4'. x = 1.25 Simplifying x = 1.25

Subproblem 2

Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 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 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5

Solution

x = {1.25, 5}

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