(4x+1)(-3x+9)=

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Solution for (4x+1)(-3x+9)= equation: 


Simplifying
(4x + 1)(-3x + 9) = 0

Reorder the terms:
(1 + 4x)(-3x + 9) = 0

Reorder the terms:
(1 + 4x)(9 + -3x) = 0

Multiply (1 + 4x) * (9 + -3x)
(1(9 + -3x) + 4x * (9 + -3x)) = 0
((9 * 1 + -3x * 1) + 4x * (9 + -3x)) = 0
((9 + -3x) + 4x * (9 + -3x)) = 0
(9 + -3x + (9 * 4x + -3x * 4x)) = 0
(9 + -3x + (36x + -12x2)) = 0

Combine like terms: -3x + 36x = 33x
(9 + 33x + -12x2) = 0

Solving
9 + 33x + -12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(3 + 11x + -4x2) = 0

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

Ignore the factor 3.

Subproblem 1
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

Subproblem 2
Set the factor '(1 + 4x)' equal to zero and attempt to solve:

Simplifying
1 + 4x = 0

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

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

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

Divide each side by '4'.
x = -0.25

Simplifying
x = -0.25
Solution
x = {3, -0.25}

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