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

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


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

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

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

Multiply (7 + 2x) * (-2 + 5x)
3(7(-2 + 5x) + 2x * (-2 + 5x)) = 0
3((-2 * 7 + 5x * 7) + 2x * (-2 + 5x)) = 0
3((-14 + 35x) + 2x * (-2 + 5x)) = 0
3(-14 + 35x + (-2 * 2x + 5x * 2x)) = 0
3(-14 + 35x + (-4x + 10x2)) = 0

Combine like terms: 35x + -4x = 31x
3(-14 + 31x + 10x2) = 0
(-14 * 3 + 31x * 3 + 10x2 * 3) = 0
(-42 + 93x + 30x2) = 0

Solving
-42 + 93x + 30x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-14 + 31x + 10x2) = 0

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

Ignore the factor 3.

Subproblem 1
Set the factor '(-7 + -2x)' equal to zero and attempt to solve:

Simplifying
-7 + -2x = 0

Solving
-7 + -2x = 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 + -2x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -2x = 0 + 7
-2x = 0 + 7

Combine like terms: 0 + 7 = 7
-2x = 7

Divide each side by '-2'.
x = -3.5

Simplifying
x = -3.5

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

Simplifying
2 + -5x = 0

Solving
2 + -5x = 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 + -5x = 0 + -2

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

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

Divide each side by '-5'.
x = 0.4

Simplifying
x = 0.4
Solution
x = {-3.5, 0.4}

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