(3x-4)(7x+5)=0

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Solution for (3x-4)(7x+5)=0 equation: 


Simplifying
(3x + -4)(7x + 5) = 0

Reorder the terms:
(-4 + 3x)(7x + 5) = 0

Reorder the terms:
(-4 + 3x)(5 + 7x) = 0

Multiply (-4 + 3x) * (5 + 7x)
(-4(5 + 7x) + 3x * (5 + 7x)) = 0
((5 * -4 + 7x * -4) + 3x * (5 + 7x)) = 0
((-20 + -28x) + 3x * (5 + 7x)) = 0
(-20 + -28x + (5 * 3x + 7x * 3x)) = 0
(-20 + -28x + (15x + 21x2)) = 0

Combine like terms: -28x + 15x = -13x
(-20 + -13x + 21x2) = 0

Solving
-20 + -13x + 21x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-5 + -7x)(4 + -3x) = 0


Subproblem 1
Set the factor '(-5 + -7x)' equal to zero and attempt to solve:

Simplifying
-5 + -7x = 0

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

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

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

Divide each side by '-7'.
x = -0.7142857143

Simplifying
x = -0.7142857143

Subproblem 2
Set the factor '(4 + -3x)' equal to zero and attempt to solve:

Simplifying
4 + -3x = 0

Solving
4 + -3x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -3x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -3x = 0 + -4
-3x = 0 + -4

Combine like terms: 0 + -4 = -4
-3x = -4

Divide each side by '-3'.
x = 1.333333333

Simplifying
x = 1.333333333
Solution
x = {-0.7142857143, 1.333333333}

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