4x(2x+3)6x(-7x-2)=0

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Solution for 4x(2x+3)6x(-7x-2)=0 equation:


Simplifying
4x(2x + 3) * 6x(-7x + -2) = 0

Reorder the terms:
4x(3 + 2x) * 6x(-7x + -2) = 0

Reorder the terms:
4x(3 + 2x) * 6x(-2 + -7x) = 0

Reorder the terms for easier multiplication:
4 * 6x * x(3 + 2x)(-2 + -7x) = 0

Multiply 4 * 6
24x * x(3 + 2x)(-2 + -7x) = 0

Multiply x * x
24x2(3 + 2x)(-2 + -7x) = 0

Multiply (3 + 2x) * (-2 + -7x)
24x2(3(-2 + -7x) + 2x * (-2 + -7x)) = 0
24x2((-2 * 3 + -7x * 3) + 2x * (-2 + -7x)) = 0
24x2((-6 + -21x) + 2x * (-2 + -7x)) = 0
24x2(-6 + -21x + (-2 * 2x + -7x * 2x)) = 0
24x2(-6 + -21x + (-4x + -14x2)) = 0

Combine like terms: -21x + -4x = -25x
24x2(-6 + -25x + -14x2) = 0
(-6 * 24x2 + -25x * 24x2 + -14x2 * 24x2) = 0
(-144x2 + -600x3 + -336x4) = 0

Solving
-144x2 + -600x3 + -336x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-24x2'.
-24x2(6 + 25x + 14x2) = 0

Factor a trinomial.
-24x2((3 + 2x)(2 + 7x)) = 0

Ignore the factor -24.

Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve:

Simplifying
x2 = 0

Solving
x2 = 0

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

Simplifying
x2 = 0

Take the square root of each side:
x = {0}

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

Simplifying
3 + 2x = 0

Solving
3 + 2x = 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 + 2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2x = 0 + -3
2x = 0 + -3

Combine like terms: 0 + -3 = -3
2x = -3

Divide each side by '2'.
x = -1.5

Simplifying
x = -1.5

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

Simplifying
2 + 7x = 0

Solving
2 + 7x = 0

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

Add '-2' to each side of the equation.
2 + -2 + 7x = 0 + -2

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

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

Divide each side by '7'.
x = -0.2857142857

Simplifying
x = -0.2857142857
Solution
x = {0, -1.5, -0.2857142857}

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