(2X+5)(4X-2)=

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Solution for (2X+5)(4X-2)= equation:


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

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

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

Multiply (5 + 2X) * (-2 + 4X)
(5(-2 + 4X) + 2X * (-2 + 4X)) = 0
((-2 * 5 + 4X * 5) + 2X * (-2 + 4X)) = 0
((-10 + 20X) + 2X * (-2 + 4X)) = 0
(-10 + 20X + (-2 * 2X + 4X * 2X)) = 0
(-10 + 20X + (-4X + 8X2)) = 0

Combine like terms: 20X + -4X = 16X
(-10 + 16X + 8X2) = 0

Solving
-10 + 16X + 8X2 = 0

Solving for variable 'X'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + 8X + 4X2) = 0

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

Ignore the factor 2.

Subproblem 1

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

Subproblem 2

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

Solution

X = {-2.5, 0.5}

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