8(3x-7)(2x+5)=0

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Solution for 8(3x-7)(2x+5)=0 equation: 


Simplifying
8(3x + -7)(2x + 5) = 0

Reorder the terms:
8(-7 + 3x)(2x + 5) = 0

Reorder the terms:
8(-7 + 3x)(5 + 2x) = 0

Multiply (-7 + 3x) * (5 + 2x)
8(-7(5 + 2x) + 3x * (5 + 2x)) = 0
8((5 * -7 + 2x * -7) + 3x * (5 + 2x)) = 0
8((-35 + -14x) + 3x * (5 + 2x)) = 0
8(-35 + -14x + (5 * 3x + 2x * 3x)) = 0
8(-35 + -14x + (15x + 6x2)) = 0

Combine like terms: -14x + 15x = 1x
8(-35 + 1x + 6x2) = 0
(-35 * 8 + 1x * 8 + 6x2 * 8) = 0
(-280 + 8x + 48x2) = 0

Solving
-280 + 8x + 48x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '8'.
8(-35 + x + 6x2) = 0

Factor a trinomial.
8((-5 + -2x)(7 + -3x)) = 0

Ignore the factor 8.

Subproblem 1
Set the factor '(-5 + -2x)' equal to zero and attempt to solve:

Simplifying
-5 + -2x = 0

Solving
-5 + -2x = 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 + -2x = 0 + 5

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

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

Divide each side by '-2'.
x = -2.5

Simplifying
x = -2.5

Subproblem 2
Set the factor '(7 + -3x)' equal to zero and attempt to solve:

Simplifying
7 + -3x = 0

Solving
7 + -3x = 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 + -3x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -3x = 0 + -7
-3x = 0 + -7

Combine like terms: 0 + -7 = -7
-3x = -7

Divide each side by '-3'.
x = 2.333333333

Simplifying
x = 2.333333333
Solution
x = {-2.5, 2.333333333}

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