5(10x-10)x=-5(-4x+4)

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Solution for 5(10x-10)x=-5(-4x+4) equation:


Simplifying
5(10x + -10) * x = -5(-4x + 4)

Reorder the terms:
5(-10 + 10x) * x = -5(-4x + 4)

Reorder the terms for easier multiplication:
5x(-10 + 10x) = -5(-4x + 4)
(-10 * 5x + 10x * 5x) = -5(-4x + 4)
(-50x + 50x2) = -5(-4x + 4)

Reorder the terms:
-50x + 50x2 = -5(4 + -4x)
-50x + 50x2 = (4 * -5 + -4x * -5)
-50x + 50x2 = (-20 + 20x)

Solving
-50x + 50x2 = -20 + 20x

Solving for variable 'x'.

Reorder the terms:
20 + -50x + -20x + 50x2 = -20 + 20x + 20 + -20x

Combine like terms: -50x + -20x = -70x
20 + -70x + 50x2 = -20 + 20x + 20 + -20x

Reorder the terms:
20 + -70x + 50x2 = -20 + 20 + 20x + -20x

Combine like terms: -20 + 20 = 0
20 + -70x + 50x2 = 0 + 20x + -20x
20 + -70x + 50x2 = 20x + -20x

Combine like terms: 20x + -20x = 0
20 + -70x + 50x2 = 0

Factor out the Greatest Common Factor (GCF), '10'.
10(2 + -7x + 5x2) = 0

Factor a trinomial.
10((2 + -5x)(1 + -1x)) = 0

Ignore the factor 10.

Subproblem 1

Set the factor '(2 + -5x)' equal to zero and attempt to solve: Simplifying 2 + -5x = 0 Solving 2 + -5x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -5x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -5x = 0 + -2 -5x = 0 + -2 Combine like terms: 0 + -2 = -2 -5x = -2 Divide each side by '-5'. x = 0.4 Simplifying x = 0.4

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 = {0.4, 1}

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