(2x-1)(x+3)=29x-75

Solution for (2x-1)(x+3)=29x-75 equation:

Simplifying
(2x + -1)(x + 3) = 29x + -75

Reorder the terms:
(-1 + 2x)(x + 3) = 29x + -75

Reorder the terms:
(-1 + 2x)(3 + x) = 29x + -75

Multiply (-1 + 2x) * (3 + x)
(-1(3 + x) + 2x * (3 + x)) = 29x + -75
((3 * -1 + x * -1) + 2x * (3 + x)) = 29x + -75
((-3 + -1x) + 2x * (3 + x)) = 29x + -75
(-3 + -1x + (3 * 2x + x * 2x)) = 29x + -75
(-3 + -1x + (6x + 2x2)) = 29x + -75

Combine like terms: -1x + 6x = 5x
(-3 + 5x + 2x2) = 29x + -75

Reorder the terms:
-3 + 5x + 2x2 = -75 + 29x

Solving
-3 + 5x + 2x2 = -75 + 29x

Solving for variable 'x'.

Reorder the terms:
-3 + 75 + 5x + -29x + 2x2 = -75 + 29x + 75 + -29x

Combine like terms: -3 + 75 = 72
72 + 5x + -29x + 2x2 = -75 + 29x + 75 + -29x

Combine like terms: 5x + -29x = -24x
72 + -24x + 2x2 = -75 + 29x + 75 + -29x

Reorder the terms:
72 + -24x + 2x2 = -75 + 75 + 29x + -29x

Combine like terms: -75 + 75 = 0
72 + -24x + 2x2 = 0 + 29x + -29x
72 + -24x + 2x2 = 29x + -29x

Combine like terms: 29x + -29x = 0
72 + -24x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(36 + -12x + x2) = 0

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

Ignore the factor 2.
Subproblem 1
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
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 = {6, 6}