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

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


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

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

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

Multiply (-5 + 2x) * (10 + x)
(-5(10 + x) + 2x * (10 + x)) = 0
((10 * -5 + x * -5) + 2x * (10 + x)) = 0
((-50 + -5x) + 2x * (10 + x)) = 0
(-50 + -5x + (10 * 2x + x * 2x)) = 0
(-50 + -5x + (20x + 2x2)) = 0

Combine like terms: -5x + 20x = 15x
(-50 + 15x + 2x2) = 0

Solving
-50 + 15x + 2x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-10 + -1x)(5 + -2x) = 0


Subproblem 1
Set the factor '(-10 + -1x)' equal to zero and attempt to solve:

Simplifying
-10 + -1x = 0

Solving
-10 + -1x = 0

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

Add '10' to each side of the equation.
-10 + 10 + -1x = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -1x = 0 + 10
-1x = 0 + 10

Combine like terms: 0 + 10 = 10
-1x = 10

Divide each side by '-1'.
x = -10

Simplifying
x = -10

Subproblem 2
Set the factor '(5 + -2x)' equal to zero and attempt to solve:

Simplifying
5 + -2x = 0

Solving
5 + -2x = 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 + -2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2x = 0 + -5
-2x = 0 + -5

Combine like terms: 0 + -5 = -5
-2x = -5

Divide each side by '-2'.
x = 2.5

Simplifying
x = 2.5
Solution
x = {-10, 2.5}

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