4(3x-6)(2x-3)-7(x-2)=0

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Solution for 4(3x-6)(2x-3)-7(x-2)=0 equation: 


Simplifying
4(3x + -6)(2x + -3) + -7(x + -2) = 0

Reorder the terms:
4(-6 + 3x)(2x + -3) + -7(x + -2) = 0

Reorder the terms:
4(-6 + 3x)(-3 + 2x) + -7(x + -2) = 0

Multiply (-6 + 3x) * (-3 + 2x)
4(-6(-3 + 2x) + 3x * (-3 + 2x)) + -7(x + -2) = 0
4((-3 * -6 + 2x * -6) + 3x * (-3 + 2x)) + -7(x + -2) = 0
4((18 + -12x) + 3x * (-3 + 2x)) + -7(x + -2) = 0
4(18 + -12x + (-3 * 3x + 2x * 3x)) + -7(x + -2) = 0
4(18 + -12x + (-9x + 6x2)) + -7(x + -2) = 0

Combine like terms: -12x + -9x = -21x
4(18 + -21x + 6x2) + -7(x + -2) = 0
(18 * 4 + -21x * 4 + 6x2 * 4) + -7(x + -2) = 0
(72 + -84x + 24x2) + -7(x + -2) = 0

Reorder the terms:
72 + -84x + 24x2 + -7(-2 + x) = 0
72 + -84x + 24x2 + (-2 * -7 + x * -7) = 0
72 + -84x + 24x2 + (14 + -7x) = 0

Reorder the terms:
72 + 14 + -84x + -7x + 24x2 = 0

Combine like terms: 72 + 14 = 86
86 + -84x + -7x + 24x2 = 0

Combine like terms: -84x + -7x = -91x
86 + -91x + 24x2 = 0

Solving
86 + -91x + 24x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(43 + -24x)(2 + -1x) = 0


Subproblem 1
Set the factor '(43 + -24x)' equal to zero and attempt to solve:

Simplifying
43 + -24x = 0

Solving
43 + -24x = 0

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

Add '-43' to each side of the equation.
43 + -43 + -24x = 0 + -43

Combine like terms: 43 + -43 = 0
0 + -24x = 0 + -43
-24x = 0 + -43

Combine like terms: 0 + -43 = -43
-24x = -43

Divide each side by '-24'.
x = 1.791666667

Simplifying
x = 1.791666667

Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {1.791666667, 2}

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