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

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


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

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

Multiply (2 + -3x) * (3 + 5x)
5(2(3 + 5x) + -3x * (3 + 5x)) = 0
5((3 * 2 + 5x * 2) + -3x * (3 + 5x)) = 0
5((6 + 10x) + -3x * (3 + 5x)) = 0
5(6 + 10x + (3 * -3x + 5x * -3x)) = 0
5(6 + 10x + (-9x + -15x2)) = 0

Combine like terms: 10x + -9x = 1x
5(6 + 1x + -15x2) = 0
(6 * 5 + 1x * 5 + -15x2 * 5) = 0
(30 + 5x + -75x2) = 0

Solving
30 + 5x + -75x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(6 + x + -15x2) = 0

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

Ignore the factor 5.

Subproblem 1
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

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 = {0.6666666667, -0.6}

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