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

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

Simplifying
(2x + -3)(7x + 7) = 0

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

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

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

Combine like terms: -21x + 14x = -7x
(-21 + -7x + 14x2) = 0

Solving
-21 + -7x + 14x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '7'.
7(-3 + -1x + 2x2) = 0

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

Ignore the factor 7.
Subproblem 1
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
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
Solution
x = {-1, 1.5}