(2x-5)*(x-1)=0

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Solution for (2x-5)*(x-1)=0 equation:


Simplifying
(2x + -5)(x + -1) = 0

Reorder the terms:
(-5 + 2x)(x + -1) = 0

Reorder the terms:
(-5 + 2x)(-1 + x) = 0

Multiply (-5 + 2x) * (-1 + x)
(-5(-1 + x) + 2x * (-1 + x)) = 0
((-1 * -5 + x * -5) + 2x * (-1 + x)) = 0
((5 + -5x) + 2x * (-1 + x)) = 0
(5 + -5x + (-1 * 2x + x * 2x)) = 0
(5 + -5x + (-2x + 2x2)) = 0

Combine like terms: -5x + -2x = -7x
(5 + -7x + 2x2) = 0

Solving
5 + -7x + 2x2 = 0

Solving for variable 'x'.

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

Subproblem 1

Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1

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 = {1, 2.5}

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