(5x-7)(3x+10)=0

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Solution for (5x-7)(3x+10)=0 equation: 


Simplifying
(5x + -7)(3x + 10) = 0

Reorder the terms:
(-7 + 5x)(3x + 10) = 0

Reorder the terms:
(-7 + 5x)(10 + 3x) = 0

Multiply (-7 + 5x) * (10 + 3x)
(-7(10 + 3x) + 5x * (10 + 3x)) = 0
((10 * -7 + 3x * -7) + 5x * (10 + 3x)) = 0
((-70 + -21x) + 5x * (10 + 3x)) = 0
(-70 + -21x + (10 * 5x + 3x * 5x)) = 0
(-70 + -21x + (50x + 15x2)) = 0

Combine like terms: -21x + 50x = 29x
(-70 + 29x + 15x2) = 0

Solving
-70 + 29x + 15x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-10 + -3x)(7 + -5x) = 0


Subproblem 1
Set the factor '(-10 + -3x)' equal to zero and attempt to solve:

Simplifying
-10 + -3x = 0

Solving
-10 + -3x = 0

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

Add '10' to each side of the equation.
-10 + 10 + -3x = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -3x = 0 + 10
-3x = 0 + 10

Combine like terms: 0 + 10 = 10
-3x = 10

Divide each side by '-3'.
x = -3.333333333

Simplifying
x = -3.333333333

Subproblem 2
Set the factor '(7 + -5x)' equal to zero and attempt to solve:

Simplifying
7 + -5x = 0

Solving
7 + -5x = 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 + -5x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -5x = 0 + -7
-5x = 0 + -7

Combine like terms: 0 + -7 = -7
-5x = -7

Divide each side by '-5'.
x = 1.4

Simplifying
x = 1.4
Solution
x = {-3.333333333, 1.4}

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