6(2x-3)(2x-3)=7(2x-3)+3

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Solution for 6(2x-3)(2x-3)=7(2x-3)+3 equation: 


Simplifying
6(2x + -3)(2x + -3) = 7(2x + -3) + 3

Reorder the terms:
6(-3 + 2x)(2x + -3) = 7(2x + -3) + 3

Reorder the terms:
6(-3 + 2x)(-3 + 2x) = 7(2x + -3) + 3

Multiply (-3 + 2x) * (-3 + 2x)
6(-3(-3 + 2x) + 2x * (-3 + 2x)) = 7(2x + -3) + 3
6((-3 * -3 + 2x * -3) + 2x * (-3 + 2x)) = 7(2x + -3) + 3
6((9 + -6x) + 2x * (-3 + 2x)) = 7(2x + -3) + 3
6(9 + -6x + (-3 * 2x + 2x * 2x)) = 7(2x + -3) + 3
6(9 + -6x + (-6x + 4x2)) = 7(2x + -3) + 3

Combine like terms: -6x + -6x = -12x
6(9 + -12x + 4x2) = 7(2x + -3) + 3
(9 * 6 + -12x * 6 + 4x2 * 6) = 7(2x + -3) + 3
(54 + -72x + 24x2) = 7(2x + -3) + 3

Reorder the terms:
54 + -72x + 24x2 = 7(-3 + 2x) + 3
54 + -72x + 24x2 = (-3 * 7 + 2x * 7) + 3
54 + -72x + 24x2 = (-21 + 14x) + 3

Reorder the terms:
54 + -72x + 24x2 = -21 + 3 + 14x

Combine like terms: -21 + 3 = -18
54 + -72x + 24x2 = -18 + 14x

Solving
54 + -72x + 24x2 = -18 + 14x

Solving for variable 'x'.

Reorder the terms:
54 + 18 + -72x + -14x + 24x2 = -18 + 14x + 18 + -14x

Combine like terms: 54 + 18 = 72
72 + -72x + -14x + 24x2 = -18 + 14x + 18 + -14x

Combine like terms: -72x + -14x = -86x
72 + -86x + 24x2 = -18 + 14x + 18 + -14x

Reorder the terms:
72 + -86x + 24x2 = -18 + 18 + 14x + -14x

Combine like terms: -18 + 18 = 0
72 + -86x + 24x2 = 0 + 14x + -14x
72 + -86x + 24x2 = 14x + -14x

Combine like terms: 14x + -14x = 0
72 + -86x + 24x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(36 + -43x + 12x2) = 0

Factor a trinomial.
2((4 + -3x)(9 + -4x)) = 0

Ignore the factor 2.

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 '(9 + -4x)' equal to zero and attempt to solve:

Simplifying
9 + -4x = 0

Solving
9 + -4x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -4x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -4x = 0 + -9
-4x = 0 + -9

Combine like terms: 0 + -9 = -9
-4x = -9

Divide each side by '-4'.
x = 2.25

Simplifying
x = 2.25
Solution
x = {1.333333333, 2.25}

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