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

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


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

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

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

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

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

Solving
-14 + -29x + 15x2 = 0

Solving for variable 'x'.

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


Subproblem 1
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

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
Solution
x = {-0.4, 2.333333333}

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