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

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


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

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

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

Multiply (3 + 3x) * (-3 + 5x)
(3(-3 + 5x) + 3x * (-3 + 5x)) = 0
((-3 * 3 + 5x * 3) + 3x * (-3 + 5x)) = 0
((-9 + 15x) + 3x * (-3 + 5x)) = 0
(-9 + 15x + (-3 * 3x + 5x * 3x)) = 0
(-9 + 15x + (-9x + 15x2)) = 0

Combine like terms: 15x + -9x = 6x
(-9 + 6x + 15x2) = 0

Solving
-9 + 6x + 15x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-3 + 2x + 5x2) = 0

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

Ignore the factor 3.

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

Simplifying
-1 + -1x = 0

Solving
-1 + -1x = 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 + -1x = 0 + 1

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

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

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

Simplifying
x = -1

Subproblem 2
Set the factor '(3 + -5x)' equal to zero and attempt to solve:

Simplifying
3 + -5x = 0

Solving
3 + -5x = 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 + -5x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -5x = 0 + -3
-5x = 0 + -3

Combine like terms: 0 + -3 = -3
-5x = -3

Divide each side by '-5'.
x = 0.6

Simplifying
x = 0.6
Solution
x = {-1, 0.6}

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