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

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


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

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

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

Multiply (5 + x) * (-10 + 8x)
(5(-10 + 8x) + x(-10 + 8x)) = 0
((-10 * 5 + 8x * 5) + x(-10 + 8x)) = 0
((-50 + 40x) + x(-10 + 8x)) = 0
(-50 + 40x + (-10 * x + 8x * x)) = 0
(-50 + 40x + (-10x + 8x2)) = 0

Combine like terms: 40x + -10x = 30x
(-50 + 30x + 8x2) = 0

Solving
-50 + 30x + 8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-25 + 15x + 4x2) = 0

Factor a trinomial.
2((-5 + -1x)(5 + -4x)) = 0

Ignore the factor 2.

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 '(5 + -4x)' equal to zero and attempt to solve:

Simplifying
5 + -4x = 0

Solving
5 + -4x = 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 + -4x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -4x = 0 + -5
-4x = 0 + -5

Combine like terms: 0 + -5 = -5
-4x = -5

Divide each side by '-4'.
x = 1.25

Simplifying
x = 1.25
Solution
x = {-5, 1.25}

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