[2x-3][x-5]=0

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Solution for [2x-3][x-5]=0 equation:


Simplifying
[2x + -3][x + -5] = 0

Reorder the terms:
[-3 + 2x][x + -5] = 0

Reorder the terms:
[-3 + 2x][-5 + x] = 0

Multiply [-3 + 2x] * [-5 + x]
[-3[-5 + x] + 2x * [-5 + x]] = 0
[[-5 * -3 + x * -3] + 2x * [-5 + x]] = 0
[[15 + -3x] + 2x * [-5 + x]] = 0
[15 + -3x + [-5 * 2x + x * 2x]] = 0
[15 + -3x + [-10x + 2x2]] = 0

Combine like terms: -3x + -10x = -13x
[15 + -13x + 2x2] = 0

Solving
15 + -13x + 2x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(3 + -2x)(5 + -1x) = 0

Subproblem 1

Set the factor '(3 + -2x)' equal to zero and attempt to solve: Simplifying 3 + -2x = 0 Solving 3 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2x = 0 + -3 -2x = 0 + -3 Combine like terms: 0 + -3 = -3 -2x = -3 Divide each side by '-2'. x = 1.5 Simplifying x = 1.5

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 = {1.5, 5}

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