(3x-4)(5x+15)=0

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Solution for (3x-4)(5x+15)=0 equation: 


Simplifying
(3x + -4)(5x + 15) = 0

Reorder the terms:
(-4 + 3x)(5x + 15) = 0

Reorder the terms:
(-4 + 3x)(15 + 5x) = 0

Multiply (-4 + 3x) * (15 + 5x)
(-4(15 + 5x) + 3x * (15 + 5x)) = 0
((15 * -4 + 5x * -4) + 3x * (15 + 5x)) = 0
((-60 + -20x) + 3x * (15 + 5x)) = 0
(-60 + -20x + (15 * 3x + 5x * 3x)) = 0
(-60 + -20x + (45x + 15x2)) = 0

Combine like terms: -20x + 45x = 25x
(-60 + 25x + 15x2) = 0

Solving
-60 + 25x + 15x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-12 + 5x + 3x2) = 0

Factor a trinomial.
5((-3 + -1x)(4 + -3x)) = 0

Ignore the factor 5.

Subproblem 1
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

Subproblem 2
Set the factor '(4 + -3x)' equal to zero and attempt to solve:

Simplifying
4 + -3x = 0

Solving
4 + -3x = 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 + -3x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -3x = 0 + -4
-3x = 0 + -4

Combine like terms: 0 + -4 = -4
-3x = -4

Divide each side by '-3'.
x = 1.333333333

Simplifying
x = 1.333333333
Solution
x = {-3, 1.333333333}

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