(2x-1)(5x-1)+14x=0

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Solution for (2x-1)(5x-1)+14x=0 equation:


Simplifying
(2x + -1)(5x + -1) + 14x = 0

Reorder the terms:
(-1 + 2x)(5x + -1) + 14x = 0

Reorder the terms:
(-1 + 2x)(-1 + 5x) + 14x = 0

Multiply (-1 + 2x) * (-1 + 5x)
(-1(-1 + 5x) + 2x * (-1 + 5x)) + 14x = 0
((-1 * -1 + 5x * -1) + 2x * (-1 + 5x)) + 14x = 0
((1 + -5x) + 2x * (-1 + 5x)) + 14x = 0
(1 + -5x + (-1 * 2x + 5x * 2x)) + 14x = 0
(1 + -5x + (-2x + 10x2)) + 14x = 0

Combine like terms: -5x + -2x = -7x
(1 + -7x + 10x2) + 14x = 0

Reorder the terms:
1 + -7x + 14x + 10x2 = 0

Combine like terms: -7x + 14x = 7x
1 + 7x + 10x2 = 0

Solving
1 + 7x + 10x2 = 0

Solving for variable 'x'.

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

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 + 5x)' equal to zero and attempt to solve: Simplifying 1 + 5x = 0 Solving 1 + 5x = 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 + 5x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 5x = 0 + -1 5x = 0 + -1 Combine like terms: 0 + -1 = -1 5x = -1 Divide each side by '5'. x = -0.2 Simplifying x = -0.2

Solution

x = {-0.5, -0.2}

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