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

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


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

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

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

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

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

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

Solving for variable 'x'.

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

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

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

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

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

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


Subproblem 1
Set the factor '(-4 + -3x)' equal to zero and attempt to solve:

Simplifying
-4 + -3x = 0

Solving
-4 + -3x = 0

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

Add '4' to each side of the equation.
-4 + 4 + -3x = 0 + 4

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

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

Divide each side by '-3'.
x = -1.333333333

Simplifying
x = -1.333333333

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 = {-1.333333333, 1}

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