(2x-5)(x+12)=0

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Solution for (2x-5)(x+12)=0 equation: 


Simplifying
(2x + -5)(x + 12) = 0

Reorder the terms:
(-5 + 2x)(x + 12) = 0

Reorder the terms:
(-5 + 2x)(12 + x) = 0

Multiply (-5 + 2x) * (12 + x)
(-5(12 + x) + 2x * (12 + x)) = 0
((12 * -5 + x * -5) + 2x * (12 + x)) = 0
((-60 + -5x) + 2x * (12 + x)) = 0
(-60 + -5x + (12 * 2x + x * 2x)) = 0
(-60 + -5x + (24x + 2x2)) = 0

Combine like terms: -5x + 24x = 19x
(-60 + 19x + 2x2) = 0

Solving
-60 + 19x + 2x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-12 + -1x)(5 + -2x) = 0


Subproblem 1
Set the factor '(-12 + -1x)' equal to zero and attempt to solve:

Simplifying
-12 + -1x = 0

Solving
-12 + -1x = 0

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

Add '12' to each side of the equation.
-12 + 12 + -1x = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -1x = 0 + 12
-1x = 0 + 12

Combine like terms: 0 + 12 = 12
-1x = 12

Divide each side by '-1'.
x = -12

Simplifying
x = -12

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 = {-12, 2.5}

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