(2x-14)(x+5)=90

Solution for (2x-14)(x+5)=90 equation:

Simplifying
(2x + -14)(x + 5) = 90

Reorder the terms:
(-14 + 2x)(x + 5) = 90

Reorder the terms:
(-14 + 2x)(5 + x) = 90

Multiply (-14 + 2x) * (5 + x)
(-14(5 + x) + 2x * (5 + x)) = 90
((5 * -14 + x * -14) + 2x * (5 + x)) = 90
((-70 + -14x) + 2x * (5 + x)) = 90
(-70 + -14x + (5 * 2x + x * 2x)) = 90
(-70 + -14x + (10x + 2x2)) = 90

Combine like terms: -14x + 10x = -4x
(-70 + -4x + 2x2) = 90

Solving
-70 + -4x + 2x2 = 90

Solving for variable 'x'.

Reorder the terms:
-70 + -90 + -4x + 2x2 = 90 + -90

Combine like terms: -70 + -90 = -160
-160 + -4x + 2x2 = 90 + -90

Combine like terms: 90 + -90 = 0
-160 + -4x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-80 + -2x + x2) = 0

Factor a trinomial.
2((-8 + -1x)(10 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-8 + -1x)' equal to zero and attempt to solve:

Simplifying
-8 + -1x = 0

Solving
-8 + -1x = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1x = 0 + 8
-1x = 0 + 8

Combine like terms: 0 + 8 = 8
-1x = 8

Divide each side by '-1'.
x = -8

Simplifying
x = -8
Subproblem 2
Set the factor '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Divide each side by '-1'.
x = 10

Simplifying
x = 10
Solution
x = {-8, 10}