(8x+2)(5x-10)=0

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Solution for (8x+2)(5x-10)=0 equation: 


Simplifying
(8x + 2)(5x + -10) = 0

Reorder the terms:
(2 + 8x)(5x + -10) = 0

Reorder the terms:
(2 + 8x)(-10 + 5x) = 0

Multiply (2 + 8x) * (-10 + 5x)
(2(-10 + 5x) + 8x * (-10 + 5x)) = 0
((-10 * 2 + 5x * 2) + 8x * (-10 + 5x)) = 0
((-20 + 10x) + 8x * (-10 + 5x)) = 0
(-20 + 10x + (-10 * 8x + 5x * 8x)) = 0
(-20 + 10x + (-80x + 40x2)) = 0

Combine like terms: 10x + -80x = -70x
(-20 + -70x + 40x2) = 0

Solving
-20 + -70x + 40x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '10'.
10(-2 + -7x + 4x2) = 0

Factor a trinomial.
10((-1 + -4x)(2 + -1x)) = 0

Ignore the factor 10.

Subproblem 1
Set the factor '(-1 + -4x)' equal to zero and attempt to solve:

Simplifying
-1 + -4x = 0

Solving
-1 + -4x = 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 + -4x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -4x = 0 + 1
-4x = 0 + 1

Combine like terms: 0 + 1 = 1
-4x = 1

Divide each side by '-4'.
x = -0.25

Simplifying
x = -0.25

Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 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 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-0.25, 2}

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