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

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


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

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

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

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

Combine like terms: 35x + -6x = 29x
(-14 + 29x + 15x2) = 0

Solving
-14 + 29x + 15x2 = 0

Solving for variable 'x'.

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


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 '(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 = {-2.333333333, 0.4}

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