(x-1)(2x+28)=0

Solution for (x-1)(2x+28)=0 equation:

Simplifying
(x + -1)(2x + 28) = 0

Reorder the terms:
(-1 + x)(2x + 28) = 0

Reorder the terms:
(-1 + x)(28 + 2x) = 0

Multiply (-1 + x) * (28 + 2x)
(-1(28 + 2x) + x(28 + 2x)) = 0
((28 * -1 + 2x * -1) + x(28 + 2x)) = 0
((-28 + -2x) + x(28 + 2x)) = 0
(-28 + -2x + (28 * x + 2x * x)) = 0
(-28 + -2x + (28x + 2x2)) = 0

Combine like terms: -2x + 28x = 26x
(-28 + 26x + 2x2) = 0

Solving
-28 + 26x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-14 + 13x + x2) = 0

Factor a trinomial.
2((-14 + -1x)(1 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-14 + -1x)' equal to zero and attempt to solve:

Simplifying
-14 + -1x = 0

Solving
-14 + -1x = 0

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

Add '14' to each side of the equation.
-14 + 14 + -1x = 0 + 14

Combine like terms: -14 + 14 = 0
0 + -1x = 0 + 14
-1x = 0 + 14

Combine like terms: 0 + 14 = 14
-1x = 14

Divide each side by '-1'.
x = -14

Simplifying
x = -14
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 = {-14, 1}