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

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


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

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

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

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

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

Solving
1 + -7x + 10x2 = -14x

Solving for variable 'x'.

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

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

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

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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