(3x-1)(5x+30)=0

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Solution for (3x-1)(5x+30)=0 equation: 


Simplifying
(3x + -1)(5x + 30) = 0

Reorder the terms:
(-1 + 3x)(5x + 30) = 0

Reorder the terms:
(-1 + 3x)(30 + 5x) = 0

Multiply (-1 + 3x) * (30 + 5x)
(-1(30 + 5x) + 3x * (30 + 5x)) = 0
((30 * -1 + 5x * -1) + 3x * (30 + 5x)) = 0
((-30 + -5x) + 3x * (30 + 5x)) = 0
(-30 + -5x + (30 * 3x + 5x * 3x)) = 0
(-30 + -5x + (90x + 15x2)) = 0

Combine like terms: -5x + 90x = 85x
(-30 + 85x + 15x2) = 0

Solving
-30 + 85x + 15x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-6 + 17x + 3x2) = 0

Factor a trinomial.
5((-6 + -1x)(1 + -3x)) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-6 + -1x)' equal to zero and attempt to solve:

Simplifying
-6 + -1x = 0

Solving
-6 + -1x = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1x = 0 + 6
-1x = 0 + 6

Combine like terms: 0 + 6 = 6
-1x = 6

Divide each side by '-1'.
x = -6

Simplifying
x = -6

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

Simplifying
1 + -3x = 0

Solving
1 + -3x = 0

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

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

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

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

Divide each side by '-3'.
x = 0.3333333333

Simplifying
x = 0.3333333333
Solution
x = {-6, 0.3333333333}

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