6(x+5)(8x-7)=0

Solution for 6(x+5)(8x-7)=0 equation:

Simplifying
6(x + 5)(8x + -7) = 0

Reorder the terms:
6(5 + x)(8x + -7) = 0

Reorder the terms:
6(5 + x)(-7 + 8x) = 0

Multiply (5 + x) * (-7 + 8x)
6(5(-7 + 8x) + x(-7 + 8x)) = 0
6((-7 * 5 + 8x * 5) + x(-7 + 8x)) = 0
6((-35 + 40x) + x(-7 + 8x)) = 0
6(-35 + 40x + (-7 * x + 8x * x)) = 0
6(-35 + 40x + (-7x + 8x2)) = 0

Combine like terms: 40x + -7x = 33x
6(-35 + 33x + 8x2) = 0
(-35 * 6 + 33x * 6 + 8x2 * 6) = 0
(-210 + 198x + 48x2) = 0

Solving
-210 + 198x + 48x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-35 + 33x + 8x2) = 0

Factor a trinomial.
6((-5 + -1x)(7 + -8x)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(-5 + -1x)' equal to zero and attempt to solve:

Simplifying
-5 + -1x = 0

Solving
-5 + -1x = 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 + -1x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1x = 0 + 5
-1x = 0 + 5

Combine like terms: 0 + 5 = 5
-1x = 5

Divide each side by '-1'.
x = -5

Simplifying
x = -5
Subproblem 2
Set the factor '(7 + -8x)' equal to zero and attempt to solve:

Simplifying
7 + -8x = 0

Solving
7 + -8x = 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 + -8x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -8x = 0 + -7
-8x = 0 + -7

Combine like terms: 0 + -7 = -7
-8x = -7

Divide each side by '-8'.
x = 0.875

Simplifying
x = 0.875
Solution
x = {-5, 0.875}