(6x+3)(-3x+4)=0

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Solution for (6x+3)(-3x+4)=0 equation: 


Simplifying
(6x + 3)(-3x + 4) = 0

Reorder the terms:
(3 + 6x)(-3x + 4) = 0

Reorder the terms:
(3 + 6x)(4 + -3x) = 0

Multiply (3 + 6x) * (4 + -3x)
(3(4 + -3x) + 6x * (4 + -3x)) = 0
((4 * 3 + -3x * 3) + 6x * (4 + -3x)) = 0
((12 + -9x) + 6x * (4 + -3x)) = 0
(12 + -9x + (4 * 6x + -3x * 6x)) = 0
(12 + -9x + (24x + -18x2)) = 0

Combine like terms: -9x + 24x = 15x
(12 + 15x + -18x2) = 0

Solving
12 + 15x + -18x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(4 + 5x + -6x2) = 0

Factor a trinomial.
3((4 + -3x)(1 + 2x)) = 0

Ignore the factor 3.

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 + 2x)' equal to zero and attempt to solve:

Simplifying
1 + 2x = 0

Solving
1 + 2x = 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 + 2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2x = 0 + -1
2x = 0 + -1

Combine like terms: 0 + -1 = -1
2x = -1

Divide each side by '2'.
x = -0.5

Simplifying
x = -0.5
Solution
x = {1.333333333, -0.5}

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