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

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


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

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

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

Multiply (6 + 4x) * (-7 + 3x)
(6(-7 + 3x) + 4x * (-7 + 3x)) = 0
((-7 * 6 + 3x * 6) + 4x * (-7 + 3x)) = 0
((-42 + 18x) + 4x * (-7 + 3x)) = 0
(-42 + 18x + (-7 * 4x + 3x * 4x)) = 0
(-42 + 18x + (-28x + 12x2)) = 0

Combine like terms: 18x + -28x = -10x
(-42 + -10x + 12x2) = 0

Solving
-42 + -10x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-21 + -5x + 6x2) = 0

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

Ignore the factor 2.

Subproblem 1
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

Subproblem 2
Set the factor '(7 + -3x)' equal to zero and attempt to solve:

Simplifying
7 + -3x = 0

Solving
7 + -3x = 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 + -3x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -3x = 0 + -7
-3x = 0 + -7

Combine like terms: 0 + -7 = -7
-3x = -7

Divide each side by '-3'.
x = 2.333333333

Simplifying
x = 2.333333333
Solution
x = {-1.5, 2.333333333}

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