8(2x-3)(7x+11)=0

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Solution for 8(2x-3)(7x+11)=0 equation: 


Simplifying
8(2x + -3)(7x + 11) = 0

Reorder the terms:
8(-3 + 2x)(7x + 11) = 0

Reorder the terms:
8(-3 + 2x)(11 + 7x) = 0

Multiply (-3 + 2x) * (11 + 7x)
8(-3(11 + 7x) + 2x * (11 + 7x)) = 0
8((11 * -3 + 7x * -3) + 2x * (11 + 7x)) = 0
8((-33 + -21x) + 2x * (11 + 7x)) = 0
8(-33 + -21x + (11 * 2x + 7x * 2x)) = 0
8(-33 + -21x + (22x + 14x2)) = 0

Combine like terms: -21x + 22x = 1x
8(-33 + 1x + 14x2) = 0
(-33 * 8 + 1x * 8 + 14x2 * 8) = 0
(-264 + 8x + 112x2) = 0

Solving
-264 + 8x + 112x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '8'.
8(-33 + x + 14x2) = 0

Factor a trinomial.
8((-11 + -7x)(3 + -2x)) = 0

Ignore the factor 8.

Subproblem 1
Set the factor '(-11 + -7x)' equal to zero and attempt to solve:

Simplifying
-11 + -7x = 0

Solving
-11 + -7x = 0

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

Add '11' to each side of the equation.
-11 + 11 + -7x = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -7x = 0 + 11
-7x = 0 + 11

Combine like terms: 0 + 11 = 11
-7x = 11

Divide each side by '-7'.
x = -1.571428571

Simplifying
x = -1.571428571

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 = {-1.571428571, 1.5}

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