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

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


Simplifying
(3x2 + 7x)(2x + -5) = 0

Reorder the terms:
(7x + 3x2)(2x + -5) = 0

Reorder the terms:
(7x + 3x2)(-5 + 2x) = 0

Multiply (7x + 3x2) * (-5 + 2x)
(7x * (-5 + 2x) + 3x2 * (-5 + 2x)) = 0
((-5 * 7x + 2x * 7x) + 3x2 * (-5 + 2x)) = 0
((-35x + 14x2) + 3x2 * (-5 + 2x)) = 0
(-35x + 14x2 + (-5 * 3x2 + 2x * 3x2)) = 0
(-35x + 14x2 + (-15x2 + 6x3)) = 0

Combine like terms: 14x2 + -15x2 = -1x2
(-35x + -1x2 + 6x3) = 0

Solving
-35x + -1x2 + 6x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-35 + -1x + 6x2) = 0

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


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

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

Simplifying
5 + -2x = 0

Solving
5 + -2x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2x = 0 + -5
-2x = 0 + -5

Combine like terms: 0 + -5 = -5
-2x = -5

Divide each side by '-2'.
x = 2.5

Simplifying
x = 2.5
Solution
x = {0, -2.333333333, 2.5}

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