4(2x-3)(4x+5)=0

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Solution for 4(2x-3)(4x+5)=0 equation: 


Simplifying
4(2x + -3)(4x + 5) = 0

Reorder the terms:
4(-3 + 2x)(4x + 5) = 0

Reorder the terms:
4(-3 + 2x)(5 + 4x) = 0

Multiply (-3 + 2x) * (5 + 4x)
4(-3(5 + 4x) + 2x * (5 + 4x)) = 0
4((5 * -3 + 4x * -3) + 2x * (5 + 4x)) = 0
4((-15 + -12x) + 2x * (5 + 4x)) = 0
4(-15 + -12x + (5 * 2x + 4x * 2x)) = 0
4(-15 + -12x + (10x + 8x2)) = 0

Combine like terms: -12x + 10x = -2x
4(-15 + -2x + 8x2) = 0
(-15 * 4 + -2x * 4 + 8x2 * 4) = 0
(-60 + -8x + 32x2) = 0

Solving
-60 + -8x + 32x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-15 + -2x + 8x2) = 0

Factor a trinomial.
4((-5 + -4x)(3 + -2x)) = 0

Ignore the factor 4.

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

Simplifying
-5 + -4x = 0

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

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

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

Divide each side by '-4'.
x = -1.25

Simplifying
x = -1.25

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

Simplifying
3 + -2x = 0

Solving
3 + -2x = 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 + -2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2x = 0 + -3
-2x = 0 + -3

Combine like terms: 0 + -3 = -3
-2x = -3

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5
Solution
x = {-1.25, 1.5}

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