4x(6+5x)(7+8x)=

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Solution for 4x(6+5x)(7+8x)= equation: 


Simplifying
4x(6 + 5x)(7 + 8x) = 0

Multiply (6 + 5x) * (7 + 8x)
4x(6(7 + 8x) + 5x * (7 + 8x)) = 0
4x((7 * 6 + 8x * 6) + 5x * (7 + 8x)) = 0
4x((42 + 48x) + 5x * (7 + 8x)) = 0
4x(42 + 48x + (7 * 5x + 8x * 5x)) = 0
4x(42 + 48x + (35x + 40x2)) = 0

Combine like terms: 48x + 35x = 83x
4x(42 + 83x + 40x2) = 0
(42 * 4x + 83x * 4x + 40x2 * 4x) = 0
(168x + 332x2 + 160x3) = 0

Solving
168x + 332x2 + 160x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4x'.
4x(42 + 83x + 40x2) = 0

Factor a trinomial.
4x((6 + 5x)(7 + 8x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(6 + 5x)' equal to zero and attempt to solve:

Simplifying
6 + 5x = 0

Solving
6 + 5x = 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 + 5x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 5x = 0 + -6
5x = 0 + -6

Combine like terms: 0 + -6 = -6
5x = -6

Divide each side by '5'.
x = -1.2

Simplifying
x = -1.2

Subproblem 3
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 = {0, -1.2, -0.875}

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