2(5x-3)(3x+7)=0

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Solution for 2(5x-3)(3x+7)=0 equation: 


Simplifying
2(5x + -3)(3x + 7) = 0

Reorder the terms:
2(-3 + 5x)(3x + 7) = 0

Reorder the terms:
2(-3 + 5x)(7 + 3x) = 0

Multiply (-3 + 5x) * (7 + 3x)
2(-3(7 + 3x) + 5x * (7 + 3x)) = 0
2((7 * -3 + 3x * -3) + 5x * (7 + 3x)) = 0
2((-21 + -9x) + 5x * (7 + 3x)) = 0
2(-21 + -9x + (7 * 5x + 3x * 5x)) = 0
2(-21 + -9x + (35x + 15x2)) = 0

Combine like terms: -9x + 35x = 26x
2(-21 + 26x + 15x2) = 0
(-21 * 2 + 26x * 2 + 15x2 * 2) = 0
(-42 + 52x + 30x2) = 0

Solving
-42 + 52x + 30x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-21 + 26x + 15x2) = 0

Factor a trinomial.
2((-7 + -3x)(3 + -5x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-7 + -3x)' equal to zero and attempt to solve:

Simplifying
-7 + -3x = 0

Solving
-7 + -3x = 0

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

Add '7' to each side of the equation.
-7 + 7 + -3x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -3x = 0 + 7
-3x = 0 + 7

Combine like terms: 0 + 7 = 7
-3x = 7

Divide each side by '-3'.
x = -2.333333333

Simplifying
x = -2.333333333

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 = {-2.333333333, 0.6}

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