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

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


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

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

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

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

Combine like terms: 5x + -2x = 3x
-2(-2 + 3x + 5x2) = 0
(-2 * -2 + 3x * -2 + 5x2 * -2) = 0
(4 + -6x + -10x2) = 0

Solving
4 + -6x + -10x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(2 + -3x + -5x2) = 0

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

Ignore the factor 2.

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 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

Solving
1 + x = 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 + x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + x = 0 + -1
x = 0 + -1

Combine like terms: 0 + -1 = -1
x = -1

Simplifying
x = -1
Solution
x = {0.4, -1}

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