(x+1)(4x-6)=24

Solution for (x+1)(4x-6)=24 equation:

Simplifying
(x + 1)(4x + -6) = 24

Reorder the terms:
(1 + x)(4x + -6) = 24

Reorder the terms:
(1 + x)(-6 + 4x) = 24

Multiply (1 + x) * (-6 + 4x)
(1(-6 + 4x) + x(-6 + 4x)) = 24
((-6 * 1 + 4x * 1) + x(-6 + 4x)) = 24
((-6 + 4x) + x(-6 + 4x)) = 24
(-6 + 4x + (-6 * x + 4x * x)) = 24
(-6 + 4x + (-6x + 4x2)) = 24

Combine like terms: 4x + -6x = -2x
(-6 + -2x + 4x2) = 24

Solving
-6 + -2x + 4x2 = 24

Solving for variable 'x'.

Reorder the terms:
-6 + -24 + -2x + 4x2 = 24 + -24

Combine like terms: -6 + -24 = -30
-30 + -2x + 4x2 = 24 + -24

Combine like terms: 24 + -24 = 0
-30 + -2x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-15 + -1x + 2x2) = 0

Factor a trinomial.
2((-5 + -2x)(3 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-5 + -2x)' equal to zero and attempt to solve:

Simplifying
-5 + -2x = 0

Solving
-5 + -2x = 0

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

Add '5' to each side of the equation.
-5 + 5 + -2x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -2x = 0 + 5
-2x = 0 + 5

Combine like terms: 0 + 5 = 5
-2x = 5

Divide each side by '-2'.
x = -2.5

Simplifying
x = -2.5
Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-2.5, 3}