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

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


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

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

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

Multiply (-3 + 4x) * (3 + 5x)
4(-3(3 + 5x) + 4x * (3 + 5x)) = 0
4((3 * -3 + 5x * -3) + 4x * (3 + 5x)) = 0
4((-9 + -15x) + 4x * (3 + 5x)) = 0
4(-9 + -15x + (3 * 4x + 5x * 4x)) = 0
4(-9 + -15x + (12x + 20x2)) = 0

Combine like terms: -15x + 12x = -3x
4(-9 + -3x + 20x2) = 0
(-9 * 4 + -3x * 4 + 20x2 * 4) = 0
(-36 + -12x + 80x2) = 0

Solving
-36 + -12x + 80x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-9 + -3x + 20x2) = 0

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

Ignore the factor 4.

Subproblem 1
Set the factor '(-3 + -5x)' equal to zero and attempt to solve:

Simplifying
-3 + -5x = 0

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

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

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

Divide each side by '-5'.
x = -0.6

Simplifying
x = -0.6

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

Simplifying
3 + -4x = 0

Solving
3 + -4x = 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 + -4x = 0 + -3

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

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

Divide each side by '-4'.
x = 0.75

Simplifying
x = 0.75
Solution
x = {-0.6, 0.75}

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