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

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


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

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

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

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

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

Solving
-15 + 29x + 14x2 = 0

Solving for variable 'x'.

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


Subproblem 1
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

Subproblem 2
Set the factor '(3 + -7x)' equal to zero and attempt to solve:

Simplifying
3 + -7x = 0

Solving
3 + -7x = 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 + -7x = 0 + -3

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

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

Divide each side by '-7'.
x = 0.4285714286

Simplifying
x = 0.4285714286
Solution
x = {-2.5, 0.4285714286}

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