(3x-2)(5x+5)=0

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Solution for (3x-2)(5x+5)=0 equation: 


Simplifying
(3x + -2)(5x + 5) = 0

Reorder the terms:
(-2 + 3x)(5x + 5) = 0

Reorder the terms:
(-2 + 3x)(5 + 5x) = 0

Multiply (-2 + 3x) * (5 + 5x)
(-2(5 + 5x) + 3x * (5 + 5x)) = 0
((5 * -2 + 5x * -2) + 3x * (5 + 5x)) = 0
((-10 + -10x) + 3x * (5 + 5x)) = 0
(-10 + -10x + (5 * 3x + 5x * 3x)) = 0
(-10 + -10x + (15x + 15x2)) = 0

Combine like terms: -10x + 15x = 5x
(-10 + 5x + 15x2) = 0

Solving
-10 + 5x + 15x2 = 0

Solving for variable 'x'.

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

Factor a trinomial.
5((-1 + -1x)(2 + -3x)) = 0

Ignore the factor 5.

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 '(2 + -3x)' equal to zero and attempt to solve:

Simplifying
2 + -3x = 0

Solving
2 + -3x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -3x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3x = 0 + -2
-3x = 0 + -2

Combine like terms: 0 + -2 = -2
-3x = -2

Divide each side by '-3'.
x = 0.6666666667

Simplifying
x = 0.6666666667
Solution
x = {-1, 0.6666666667}

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