7x(2x-3)+8(2x-3)=0

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Solution for 7x(2x-3)+8(2x-3)=0 equation: 


Simplifying
7x(2x + -3) + 8(2x + -3) = 0

Reorder the terms:
7x(-3 + 2x) + 8(2x + -3) = 0
(-3 * 7x + 2x * 7x) + 8(2x + -3) = 0
(-21x + 14x2) + 8(2x + -3) = 0

Reorder the terms:
-21x + 14x2 + 8(-3 + 2x) = 0
-21x + 14x2 + (-3 * 8 + 2x * 8) = 0
-21x + 14x2 + (-24 + 16x) = 0

Reorder the terms:
-24 + -21x + 16x + 14x2 = 0

Combine like terms: -21x + 16x = -5x
-24 + -5x + 14x2 = 0

Solving
-24 + -5x + 14x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-8 + -7x)(3 + -2x) = 0


Subproblem 1
Set the factor '(-8 + -7x)' equal to zero and attempt to solve:

Simplifying
-8 + -7x = 0

Solving
-8 + -7x = 0

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

Add '8' to each side of the equation.
-8 + 8 + -7x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -7x = 0 + 8
-7x = 0 + 8

Combine like terms: 0 + 8 = 8
-7x = 8

Divide each side by '-7'.
x = -1.142857143

Simplifying
x = -1.142857143

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 = {-1.142857143, 1.5}

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