(12x+7)(5x-15)=0

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Solution for (12x+7)(5x-15)=0 equation: 


Simplifying
(12x + 7)(5x + -15) = 0

Reorder the terms:
(7 + 12x)(5x + -15) = 0

Reorder the terms:
(7 + 12x)(-15 + 5x) = 0

Multiply (7 + 12x) * (-15 + 5x)
(7(-15 + 5x) + 12x * (-15 + 5x)) = 0
((-15 * 7 + 5x * 7) + 12x * (-15 + 5x)) = 0
((-105 + 35x) + 12x * (-15 + 5x)) = 0
(-105 + 35x + (-15 * 12x + 5x * 12x)) = 0
(-105 + 35x + (-180x + 60x2)) = 0

Combine like terms: 35x + -180x = -145x
(-105 + -145x + 60x2) = 0

Solving
-105 + -145x + 60x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-21 + -29x + 12x2) = 0

Factor a trinomial.
5((-7 + -12x)(3 + -1x)) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-7 + -12x)' equal to zero and attempt to solve:

Simplifying
-7 + -12x = 0

Solving
-7 + -12x = 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 + -12x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -12x = 0 + 7
-12x = 0 + 7

Combine like terms: 0 + 7 = 7
-12x = 7

Divide each side by '-12'.
x = -0.5833333333

Simplifying
x = -0.5833333333

Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-0.5833333333, 3}

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