2(x+6)(4x-7)=0

Solution for 2(x+6)(4x-7)=0 equation:

Simplifying
2(x + 6)(4x + -7) = 0

Reorder the terms:
2(6 + x)(4x + -7) = 0

Reorder the terms:
2(6 + x)(-7 + 4x) = 0

Multiply (6 + x) * (-7 + 4x)
2(6(-7 + 4x) + x(-7 + 4x)) = 0
2((-7 * 6 + 4x * 6) + x(-7 + 4x)) = 0
2((-42 + 24x) + x(-7 + 4x)) = 0
2(-42 + 24x + (-7 * x + 4x * x)) = 0
2(-42 + 24x + (-7x + 4x2)) = 0

Combine like terms: 24x + -7x = 17x
2(-42 + 17x + 4x2) = 0
(-42 * 2 + 17x * 2 + 4x2 * 2) = 0
(-84 + 34x + 8x2) = 0

Solving
-84 + 34x + 8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-42 + 17x + 4x2) = 0

Factor a trinomial.
2((-6 + -1x)(7 + -4x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-6 + -1x)' equal to zero and attempt to solve:

Simplifying
-6 + -1x = 0

Solving
-6 + -1x = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1x = 0 + 6
-1x = 0 + 6

Combine like terms: 0 + 6 = 6
-1x = 6

Divide each side by '-1'.
x = -6

Simplifying
x = -6
Subproblem 2
Set the factor '(7 + -4x)' equal to zero and attempt to solve:

Simplifying
7 + -4x = 0

Solving
7 + -4x = 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 + -4x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -4x = 0 + -7
-4x = 0 + -7

Combine like terms: 0 + -7 = -7
-4x = -7

Divide each side by '-4'.
x = 1.75

Simplifying
x = 1.75
Solution
x = {-6, 1.75}