(3x-12)(5x+35)=0

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Solution for (3x-12)(5x+35)=0 equation: 


Simplifying
(3x + -12)(5x + 35) = 0

Reorder the terms:
(-12 + 3x)(5x + 35) = 0

Reorder the terms:
(-12 + 3x)(35 + 5x) = 0

Multiply (-12 + 3x) * (35 + 5x)
(-12(35 + 5x) + 3x * (35 + 5x)) = 0
((35 * -12 + 5x * -12) + 3x * (35 + 5x)) = 0
((-420 + -60x) + 3x * (35 + 5x)) = 0
(-420 + -60x + (35 * 3x + 5x * 3x)) = 0
(-420 + -60x + (105x + 15x2)) = 0

Combine like terms: -60x + 105x = 45x
(-420 + 45x + 15x2) = 0

Solving
-420 + 45x + 15x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '15'.
15(-28 + 3x + x2) = 0

Factor a trinomial.
15((-7 + -1x)(4 + -1x)) = 0

Ignore the factor 15.

Subproblem 1
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

Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-7, 4}

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