(2x+3)(3x-4)=143

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Solution for (2x+3)(3x-4)=143 equation: 


Simplifying
(2x + 3)(3x + -4) = 143

Reorder the terms:
(3 + 2x)(3x + -4) = 143

Reorder the terms:
(3 + 2x)(-4 + 3x) = 143

Multiply (3 + 2x) * (-4 + 3x)
(3(-4 + 3x) + 2x * (-4 + 3x)) = 143
((-4 * 3 + 3x * 3) + 2x * (-4 + 3x)) = 143
((-12 + 9x) + 2x * (-4 + 3x)) = 143
(-12 + 9x + (-4 * 2x + 3x * 2x)) = 143
(-12 + 9x + (-8x + 6x2)) = 143

Combine like terms: 9x + -8x = 1x
(-12 + 1x + 6x2) = 143

Solving
-12 + 1x + 6x2 = 143

Solving for variable 'x'.

Reorder the terms:
-12 + -143 + 1x + 6x2 = 143 + -143

Combine like terms: -12 + -143 = -155
-155 + 1x + 6x2 = 143 + -143

Combine like terms: 143 + -143 = 0
-155 + 1x + 6x2 = 0

Factor a trinomial.
(-31 + -6x)(5 + -1x) = 0


Subproblem 1
Set the factor '(-31 + -6x)' equal to zero and attempt to solve:

Simplifying
-31 + -6x = 0

Solving
-31 + -6x = 0

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

Add '31' to each side of the equation.
-31 + 31 + -6x = 0 + 31

Combine like terms: -31 + 31 = 0
0 + -6x = 0 + 31
-6x = 0 + 31

Combine like terms: 0 + 31 = 31
-6x = 31

Divide each side by '-6'.
x = -5.166666667

Simplifying
x = -5.166666667

Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-5.166666667, 5}

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