-3x(4x-5)(2x+7)=

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Solution for -3x(4x-5)(2x+7)= equation: 


Simplifying
-3x(4x + -5)(2x + 7) = 0

Reorder the terms:
-3x(-5 + 4x)(2x + 7) = 0

Reorder the terms:
-3x(-5 + 4x)(7 + 2x) = 0

Multiply (-5 + 4x) * (7 + 2x)
-3x(-5(7 + 2x) + 4x * (7 + 2x)) = 0
-3x((7 * -5 + 2x * -5) + 4x * (7 + 2x)) = 0
-3x((-35 + -10x) + 4x * (7 + 2x)) = 0
-3x(-35 + -10x + (7 * 4x + 2x * 4x)) = 0
-3x(-35 + -10x + (28x + 8x2)) = 0

Combine like terms: -10x + 28x = 18x
-3x(-35 + 18x + 8x2) = 0
(-35 * -3x + 18x * -3x + 8x2 * -3x) = 0
(105x + -54x2 + -24x3) = 0

Solving
105x + -54x2 + -24x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x'.
3x(35 + -18x + -8x2) = 0

Factor a trinomial.
3x((5 + -4x)(7 + 2x)) = 0

Ignore the factor 3.

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 '(5 + -4x)' equal to zero and attempt to solve:

Simplifying
5 + -4x = 0

Solving
5 + -4x = 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 + -4x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -4x = 0 + -5
-4x = 0 + -5

Combine like terms: 0 + -5 = -5
-4x = -5

Divide each side by '-4'.
x = 1.25

Simplifying
x = 1.25

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

Simplifying
7 + 2x = 0

Solving
7 + 2x = 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 + 2x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 2x = 0 + -7
2x = 0 + -7

Combine like terms: 0 + -7 = -7
2x = -7

Divide each side by '2'.
x = -3.5

Simplifying
x = -3.5
Solution
x = {0, 1.25, -3.5}

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