(6x^2-14x)(x+13)=0

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Solution for (6x^2-14x)(x+13)=0 equation: 


Simplifying
(6x2 + -14x)(x + 13) = 0

Reorder the terms:
(-14x + 6x2)(x + 13) = 0

Reorder the terms:
(-14x + 6x2)(13 + x) = 0

Multiply (-14x + 6x2) * (13 + x)
(-14x * (13 + x) + 6x2 * (13 + x)) = 0
((13 * -14x + x * -14x) + 6x2 * (13 + x)) = 0
((-182x + -14x2) + 6x2 * (13 + x)) = 0
(-182x + -14x2 + (13 * 6x2 + x * 6x2)) = 0
(-182x + -14x2 + (78x2 + 6x3)) = 0

Combine like terms: -14x2 + 78x2 = 64x2
(-182x + 64x2 + 6x3) = 0

Solving
-182x + 64x2 + 6x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(-91 + 32x + 3x2) = 0

Factor a trinomial.
2x((-13 + -1x)(7 + -3x)) = 0

Ignore the factor 2.

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 '(-13 + -1x)' equal to zero and attempt to solve:

Simplifying
-13 + -1x = 0

Solving
-13 + -1x = 0

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

Add '13' to each side of the equation.
-13 + 13 + -1x = 0 + 13

Combine like terms: -13 + 13 = 0
0 + -1x = 0 + 13
-1x = 0 + 13

Combine like terms: 0 + 13 = 13
-1x = 13

Divide each side by '-1'.
x = -13

Simplifying
x = -13

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

Simplifying
7 + -3x = 0

Solving
7 + -3x = 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 + -3x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -3x = 0 + -7
-3x = 0 + -7

Combine like terms: 0 + -7 = -7
-3x = -7

Divide each side by '-3'.
x = 2.333333333

Simplifying
x = 2.333333333
Solution
x = {0, -13, 2.333333333}

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