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

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


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

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

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

Multiply (-2 + 4x) * (-5 + x)
(-2(-5 + x) + 4x * (-5 + x)) = 0
((-5 * -2 + x * -2) + 4x * (-5 + x)) = 0
((10 + -2x) + 4x * (-5 + x)) = 0
(10 + -2x + (-5 * 4x + x * 4x)) = 0
(10 + -2x + (-20x + 4x2)) = 0

Combine like terms: -2x + -20x = -22x
(10 + -22x + 4x2) = 0

Solving
10 + -22x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(5 + -11x + 2x2) = 0

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

Ignore the factor 2.

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 '(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 = {0.5, 5}

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