(4x+12)x(2x-5)=

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Solution for (4x+12)x(2x-5)= equation:


Simplifying
(4x + 12) * x(2x + -5) = 0

Reorder the terms:
(12 + 4x) * x(2x + -5) = 0

Reorder the terms:
(12 + 4x) * x(-5 + 2x) = 0

Reorder the terms for easier multiplication:
x(12 + 4x)(-5 + 2x) = 0

Multiply (12 + 4x) * (-5 + 2x)
x(12(-5 + 2x) + 4x * (-5 + 2x)) = 0
x((-5 * 12 + 2x * 12) + 4x * (-5 + 2x)) = 0
x((-60 + 24x) + 4x * (-5 + 2x)) = 0
x(-60 + 24x + (-5 * 4x + 2x * 4x)) = 0
x(-60 + 24x + (-20x + 8x2)) = 0

Combine like terms: 24x + -20x = 4x
x(-60 + 4x + 8x2) = 0
(-60 * x + 4x * x + 8x2 * x) = 0
(-60x + 4x2 + 8x3) = 0

Solving
-60x + 4x2 + 8x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4x'.
4x(-15 + x + 2x2) = 0

Factor a trinomial.
4x((-3 + -1x)(5 + -2x)) = 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 '(-3 + -1x)' equal to zero and attempt to solve:

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1x = 0 + 3
-1x = 0 + 3

Combine like terms: 0 + 3 = 3
-1x = 3

Divide each side by '-1'.
x = -3

Simplifying
x = -3

Subproblem 3
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
Solution
x = {0, -3, 2.5}

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