8(4x+3)(10x-4)=0

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Solution for 8(4x+3)(10x-4)=0 equation: 


Simplifying
8(4x + 3)(10x + -4) = 0

Reorder the terms:
8(3 + 4x)(10x + -4) = 0

Reorder the terms:
8(3 + 4x)(-4 + 10x) = 0

Multiply (3 + 4x) * (-4 + 10x)
8(3(-4 + 10x) + 4x * (-4 + 10x)) = 0
8((-4 * 3 + 10x * 3) + 4x * (-4 + 10x)) = 0
8((-12 + 30x) + 4x * (-4 + 10x)) = 0
8(-12 + 30x + (-4 * 4x + 10x * 4x)) = 0
8(-12 + 30x + (-16x + 40x2)) = 0

Combine like terms: 30x + -16x = 14x
8(-12 + 14x + 40x2) = 0
(-12 * 8 + 14x * 8 + 40x2 * 8) = 0
(-96 + 112x + 320x2) = 0

Solving
-96 + 112x + 320x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '16'.
16(-6 + 7x + 20x2) = 0

Factor a trinomial.
16((-3 + -4x)(2 + -5x)) = 0

Ignore the factor 16.

Subproblem 1
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

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

Simplifying
2 + -5x = 0

Solving
2 + -5x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + -5x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -5x = 0 + -2
-5x = 0 + -2

Combine like terms: 0 + -2 = -2
-5x = -2

Divide each side by '-5'.
x = 0.4

Simplifying
x = 0.4
Solution
x = {-0.75, 0.4}

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