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

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


Simplifying
7(x + -6)(2x + 7) = 0

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

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

Multiply (-6 + x) * (7 + 2x)
7(-6(7 + 2x) + x(7 + 2x)) = 0
7((7 * -6 + 2x * -6) + x(7 + 2x)) = 0
7((-42 + -12x) + x(7 + 2x)) = 0
7(-42 + -12x + (7 * x + 2x * x)) = 0
7(-42 + -12x + (7x + 2x2)) = 0

Combine like terms: -12x + 7x = -5x
7(-42 + -5x + 2x2) = 0
(-42 * 7 + -5x * 7 + 2x2 * 7) = 0
(-294 + -35x + 14x2) = 0

Solving
-294 + -35x + 14x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '7'.
7(-42 + -5x + 2x2) = 0

Factor a trinomial.
7((-7 + -2x)(6 + -1x)) = 0

Ignore the factor 7.

Subproblem 1
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

Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 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 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {-3.5, 6}

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