(7x-7)(6x+9)=0

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Solution for (7x-7)(6x+9)=0 equation: 


Simplifying
(7x + -7)(6x + 9) = 0

Reorder the terms:
(-7 + 7x)(6x + 9) = 0

Reorder the terms:
(-7 + 7x)(9 + 6x) = 0

Multiply (-7 + 7x) * (9 + 6x)
(-7(9 + 6x) + 7x * (9 + 6x)) = 0
((9 * -7 + 6x * -7) + 7x * (9 + 6x)) = 0
((-63 + -42x) + 7x * (9 + 6x)) = 0
(-63 + -42x + (9 * 7x + 6x * 7x)) = 0
(-63 + -42x + (63x + 42x2)) = 0

Combine like terms: -42x + 63x = 21x
(-63 + 21x + 42x2) = 0

Solving
-63 + 21x + 42x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '21'.
21(-3 + x + 2x2) = 0

Factor a trinomial.
21((-3 + -2x)(1 + -1x)) = 0

Ignore the factor 21.

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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1
Solution
x = {-1.5, 1}

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