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

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


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

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

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

Multiply (7 + 4x) * (-5 + 3x)
(7(-5 + 3x) + 4x * (-5 + 3x)) = 0
((-5 * 7 + 3x * 7) + 4x * (-5 + 3x)) = 0
((-35 + 21x) + 4x * (-5 + 3x)) = 0
(-35 + 21x + (-5 * 4x + 3x * 4x)) = 0
(-35 + 21x + (-20x + 12x2)) = 0

Combine like terms: 21x + -20x = 1x
(-35 + 1x + 12x2) = 0

Solving
-35 + 1x + 12x2 = 0

Solving for variable 'x'.

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


Subproblem 1
Set the factor '(-7 + -4x)' equal to zero and attempt to solve:

Simplifying
-7 + -4x = 0

Solving
-7 + -4x = 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 + -4x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -4x = 0 + 7
-4x = 0 + 7

Combine like terms: 0 + 7 = 7
-4x = 7

Divide each side by '-4'.
x = -1.75

Simplifying
x = -1.75

Subproblem 2
Set the factor '(5 + -3x)' equal to zero and attempt to solve:

Simplifying
5 + -3x = 0

Solving
5 + -3x = 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 + -3x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3x = 0 + -5
-3x = 0 + -5

Combine like terms: 0 + -5 = -5
-3x = -5

Divide each side by '-3'.
x = 1.666666667

Simplifying
x = 1.666666667
Solution
x = {-1.75, 1.666666667}

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