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

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


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

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

Multiply (-2 + 8x) * (10 + 2x)
(-2(10 + 2x) + 8x * (10 + 2x)) = 0
((10 * -2 + 2x * -2) + 8x * (10 + 2x)) = 0
((-20 + -4x) + 8x * (10 + 2x)) = 0
(-20 + -4x + (10 * 8x + 2x * 8x)) = 0
(-20 + -4x + (80x + 16x2)) = 0

Combine like terms: -4x + 80x = 76x
(-20 + 76x + 16x2) = 0

Solving
-20 + 76x + 16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-5 + 19x + 4x2) = 0

Factor a trinomial.
4((-5 + -1x)(1 + -4x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-5 + -1x)' equal to zero and attempt to solve:

Simplifying
-5 + -1x = 0

Solving
-5 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '5' to each side of the equation.
-5 + 5 + -1x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1x = 0 + 5
-1x = 0 + 5

Combine like terms: 0 + 5 = 5
-1x = 5

Divide each side by '-1'.
x = -5

Simplifying
x = -5

Subproblem 2
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
Solution
x = {-5, 0.25}

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