(4x-7)(6x+3)=0

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Solution for (4x-7)(6x+3)=0 equation: 


Simplifying
(4x + -7)(6x + 3) = 0

Reorder the terms:
(-7 + 4x)(6x + 3) = 0

Reorder the terms:
(-7 + 4x)(3 + 6x) = 0

Multiply (-7 + 4x) * (3 + 6x)
(-7(3 + 6x) + 4x * (3 + 6x)) = 0
((3 * -7 + 6x * -7) + 4x * (3 + 6x)) = 0
((-21 + -42x) + 4x * (3 + 6x)) = 0
(-21 + -42x + (3 * 4x + 6x * 4x)) = 0
(-21 + -42x + (12x + 24x2)) = 0

Combine like terms: -42x + 12x = -30x
(-21 + -30x + 24x2) = 0

Solving
-21 + -30x + 24x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-7 + -10x + 8x2) = 0

Factor a trinomial.
3((-1 + -2x)(7 + -4x)) = 0

Ignore the factor 3.

Subproblem 1
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

Subproblem 2
Set the factor '(7 + -4x)' equal to zero and attempt to solve:

Simplifying
7 + -4x = 0

Solving
7 + -4x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -4x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -4x = 0 + -7
-4x = 0 + -7

Combine like terms: 0 + -7 = -7
-4x = -7

Divide each side by '-4'.
x = 1.75

Simplifying
x = 1.75
Solution
x = {-0.5, 1.75}

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