(5x+25)(6x-12)=0

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Solution for (5x+25)(6x-12)=0 equation: 


Simplifying
(5x + 25)(6x + -12) = 0

Reorder the terms:
(25 + 5x)(6x + -12) = 0

Reorder the terms:
(25 + 5x)(-12 + 6x) = 0

Multiply (25 + 5x) * (-12 + 6x)
(25(-12 + 6x) + 5x * (-12 + 6x)) = 0
((-12 * 25 + 6x * 25) + 5x * (-12 + 6x)) = 0
((-300 + 150x) + 5x * (-12 + 6x)) = 0
(-300 + 150x + (-12 * 5x + 6x * 5x)) = 0
(-300 + 150x + (-60x + 30x2)) = 0

Combine like terms: 150x + -60x = 90x
(-300 + 90x + 30x2) = 0

Solving
-300 + 90x + 30x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '30'.
30(-10 + 3x + x2) = 0

Factor a trinomial.
30((-5 + -1x)(2 + -1x)) = 0

Ignore the factor 30.

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 '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-5, 2}

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