(5x-35)(x+12)=0

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Solution for (5x-35)(x+12)=0 equation: 


Simplifying
(5x + -35)(x + 12) = 0

Reorder the terms:
(-35 + 5x)(x + 12) = 0

Reorder the terms:
(-35 + 5x)(12 + x) = 0

Multiply (-35 + 5x) * (12 + x)
(-35(12 + x) + 5x * (12 + x)) = 0
((12 * -35 + x * -35) + 5x * (12 + x)) = 0
((-420 + -35x) + 5x * (12 + x)) = 0
(-420 + -35x + (12 * 5x + x * 5x)) = 0
(-420 + -35x + (60x + 5x2)) = 0

Combine like terms: -35x + 60x = 25x
(-420 + 25x + 5x2) = 0

Solving
-420 + 25x + 5x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-84 + 5x + x2) = 0

Factor a trinomial.
5((-12 + -1x)(7 + -1x)) = 0

Ignore the factor 5.

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 '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {-12, 7}

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