2(5x+1)2x=2-2(3x+1)

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Solution for 2(5x+1)2x=2-2(3x+1) equation:


Simplifying
2(5x + 1) * 2x = 2 + -2(3x + 1)

Reorder the terms:
2(1 + 5x) * 2x = 2 + -2(3x + 1)

Reorder the terms for easier multiplication:
2 * 2x(1 + 5x) = 2 + -2(3x + 1)

Multiply 2 * 2
4x(1 + 5x) = 2 + -2(3x + 1)
(1 * 4x + 5x * 4x) = 2 + -2(3x + 1)
(4x + 20x2) = 2 + -2(3x + 1)

Reorder the terms:
4x + 20x2 = 2 + -2(1 + 3x)
4x + 20x2 = 2 + (1 * -2 + 3x * -2)
4x + 20x2 = 2 + (-2 + -6x)

Combine like terms: 2 + -2 = 0
4x + 20x2 = 0 + -6x
4x + 20x2 = -6x

Solving
4x + 20x2 = -6x

Solving for variable 'x'.

Reorder the terms:
4x + 6x + 20x2 = -6x + 6x

Combine like terms: 4x + 6x = 10x
10x + 20x2 = -6x + 6x

Combine like terms: -6x + 6x = 0
10x + 20x2 = 0

Factor out the Greatest Common Factor (GCF), '10x'.
10x(1 + 2x) = 0

Ignore the factor 10.

Subproblem 1

Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0

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 = {0, -0.5}

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