0=(x+1)(-4x+3)

Solution for 0=(x+1)(-4x+3) equation:

Simplifying
0 = (x + 1)(-4x + 3)

Reorder the terms:
0 = (1 + x)(-4x + 3)

Reorder the terms:
0 = (1 + x)(3 + -4x)

Multiply (1 + x) * (3 + -4x)
0 = (1(3 + -4x) + x(3 + -4x))
0 = ((3 * 1 + -4x * 1) + x(3 + -4x))
0 = ((3 + -4x) + x(3 + -4x))
0 = (3 + -4x + (3 * x + -4x * x))
0 = (3 + -4x + (3x + -4x2))

Combine like terms: -4x + 3x = -1x
0 = (3 + -1x + -4x2)

Solving
0 = 3 + -1x + -4x2

Solving for variable 'x'.

Combine like terms: 0 + -3 = -3
-3 + x + 4x2 = 3 + -1x + -4x2 + -3 + x + 4x2

Reorder the terms:
-3 + x + 4x2 = 3 + -3 + -1x + x + -4x2 + 4x2

Combine like terms: 3 + -3 = 0
-3 + x + 4x2 = 0 + -1x + x + -4x2 + 4x2
-3 + x + 4x2 = -1x + x + -4x2 + 4x2

Combine like terms: -1x + x = 0
-3 + x + 4x2 = 0 + -4x2 + 4x2
-3 + x + 4x2 = -4x2 + 4x2

Combine like terms: -4x2 + 4x2 = 0
-3 + x + 4x2 = 0

Factor a trinomial.
(-1 + -1x)(3 + -4x) = 0

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 + -4x)' equal to zero and attempt to solve:

Simplifying
3 + -4x = 0

Solving
3 + -4x = 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 + -4x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4x = 0 + -3
-4x = 0 + -3

Combine like terms: 0 + -3 = -3
-4x = -3

Divide each side by '-4'.
x = 0.75

Simplifying
x = 0.75
Solution
x = {-1, 0.75}