(3x+1)(5x-7)=0

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Solution for (3x+1)(5x-7)=0 equation: 


Simplifying
(3x + 1)(5x + -7) = 0

Reorder the terms:
(1 + 3x)(5x + -7) = 0

Reorder the terms:
(1 + 3x)(-7 + 5x) = 0

Multiply (1 + 3x) * (-7 + 5x)
(1(-7 + 5x) + 3x * (-7 + 5x)) = 0
((-7 * 1 + 5x * 1) + 3x * (-7 + 5x)) = 0
((-7 + 5x) + 3x * (-7 + 5x)) = 0
(-7 + 5x + (-7 * 3x + 5x * 3x)) = 0
(-7 + 5x + (-21x + 15x2)) = 0

Combine like terms: 5x + -21x = -16x
(-7 + -16x + 15x2) = 0

Solving
-7 + -16x + 15x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-1 + -3x)(7 + -5x) = 0


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

Simplifying
-1 + -3x = 0

Solving
-1 + -3x = 0

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

Add '1' to each side of the equation.
-1 + 1 + -3x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -3x = 0 + 1
-3x = 0 + 1

Combine like terms: 0 + 1 = 1
-3x = 1

Divide each side by '-3'.
x = -0.3333333333

Simplifying
x = -0.3333333333

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 = {-0.3333333333, 1.4}

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