(4x+7)(6x-9)=

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Solution for (4x+7)(6x-9)= equation: 


Simplifying
(4x + 7)(6x + -9) = 0

Reorder the terms:
(7 + 4x)(6x + -9) = 0

Reorder the terms:
(7 + 4x)(-9 + 6x) = 0

Multiply (7 + 4x) * (-9 + 6x)
(7(-9 + 6x) + 4x * (-9 + 6x)) = 0
((-9 * 7 + 6x * 7) + 4x * (-9 + 6x)) = 0
((-63 + 42x) + 4x * (-9 + 6x)) = 0
(-63 + 42x + (-9 * 4x + 6x * 4x)) = 0
(-63 + 42x + (-36x + 24x2)) = 0

Combine like terms: 42x + -36x = 6x
(-63 + 6x + 24x2) = 0

Solving
-63 + 6x + 24x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-21 + 2x + 8x2) = 0

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

Ignore the factor 3.

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 '(3 + -2x)' equal to zero and attempt to solve:

Simplifying
3 + -2x = 0

Solving
3 + -2x = 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 + -2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2x = 0 + -3
-2x = 0 + -3

Combine like terms: 0 + -3 = -3
-2x = -3

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5
Solution
x = {-1.75, 1.5}

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