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

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


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

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

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

Multiply (-5 + 5x) * (-1 + 2x)
(-5(-1 + 2x) + 5x * (-1 + 2x)) = 0
((-1 * -5 + 2x * -5) + 5x * (-1 + 2x)) = 0
((5 + -10x) + 5x * (-1 + 2x)) = 0
(5 + -10x + (-1 * 5x + 2x * 5x)) = 0
(5 + -10x + (-5x + 10x2)) = 0

Combine like terms: -10x + -5x = -15x
(5 + -15x + 10x2) = 0

Solving
5 + -15x + 10x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(1 + -3x + 2x2) = 0

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

Ignore the factor 5.

Subproblem 1

Set the factor '(1 + -2x)' equal to zero and attempt to solve: Simplifying 1 + -2x = 0 Solving 1 + -2x = 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 + -2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2x = 0 + -1 -2x = 0 + -1 Combine like terms: 0 + -1 = -1 -2x = -1 Divide each side by '-2'. x = 0.5 Simplifying x = 0.5

Subproblem 2

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

Solution

x = {0.5, 1}

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