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

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


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

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

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

Multiply (-3 + 7x) * (4 + 5x)
(-3(4 + 5x) + 7x * (4 + 5x)) = 0
((4 * -3 + 5x * -3) + 7x * (4 + 5x)) = 0
((-12 + -15x) + 7x * (4 + 5x)) = 0
(-12 + -15x + (4 * 7x + 5x * 7x)) = 0
(-12 + -15x + (28x + 35x2)) = 0

Combine like terms: -15x + 28x = 13x
(-12 + 13x + 35x2) = 0

Solving
-12 + 13x + 35x2 = 0

Solving for variable 'x'.

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


Subproblem 1
Set the factor '(-4 + -5x)' equal to zero and attempt to solve:

Simplifying
-4 + -5x = 0

Solving
-4 + -5x = 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 + -5x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -5x = 0 + 4
-5x = 0 + 4

Combine like terms: 0 + 4 = 4
-5x = 4

Divide each side by '-5'.
x = -0.8

Simplifying
x = -0.8

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 = {-0.8, 0.4285714286}

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