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

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


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

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

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

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

Combine like terms: -21x + 20x = -1x
5(-35 + -1x + 12x2) = 0
(-35 * 5 + -1x * 5 + 12x2 * 5) = 0
(-175 + -5x + 60x2) = 0

Solving
-175 + -5x + 60x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-35 + -1x + 12x2) = 0

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

Ignore the factor 5.

Subproblem 1
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

Subproblem 2
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
Solution
x = {-1.666666667, 1.75}

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