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

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


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

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

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

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

Combine like terms: 42x + -24x = 18x
(-42 + 18x + 24x2) = 0

Solving
-42 + 18x + 24x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-7 + 3x + 4x2) = 0

Factor a trinomial.
6((-7 + -4x)(1 + -1x)) = 0

Ignore the factor 6.

Subproblem 1
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

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 = {-1.75, 1}

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