(2x+5)(3x-4)=9x+8

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Solution for (2x+5)(3x-4)=9x+8 equation: 


Simplifying
(2x + 5)(3x + -4) = 9x + 8

Reorder the terms:
(5 + 2x)(3x + -4) = 9x + 8

Reorder the terms:
(5 + 2x)(-4 + 3x) = 9x + 8

Multiply (5 + 2x) * (-4 + 3x)
(5(-4 + 3x) + 2x * (-4 + 3x)) = 9x + 8
((-4 * 5 + 3x * 5) + 2x * (-4 + 3x)) = 9x + 8
((-20 + 15x) + 2x * (-4 + 3x)) = 9x + 8
(-20 + 15x + (-4 * 2x + 3x * 2x)) = 9x + 8
(-20 + 15x + (-8x + 6x2)) = 9x + 8

Combine like terms: 15x + -8x = 7x
(-20 + 7x + 6x2) = 9x + 8

Reorder the terms:
-20 + 7x + 6x2 = 8 + 9x

Solving
-20 + 7x + 6x2 = 8 + 9x

Solving for variable 'x'.

Reorder the terms:
-20 + -8 + 7x + -9x + 6x2 = 8 + 9x + -8 + -9x

Combine like terms: -20 + -8 = -28
-28 + 7x + -9x + 6x2 = 8 + 9x + -8 + -9x

Combine like terms: 7x + -9x = -2x
-28 + -2x + 6x2 = 8 + 9x + -8 + -9x

Reorder the terms:
-28 + -2x + 6x2 = 8 + -8 + 9x + -9x

Combine like terms: 8 + -8 = 0
-28 + -2x + 6x2 = 0 + 9x + -9x
-28 + -2x + 6x2 = 9x + -9x

Combine like terms: 9x + -9x = 0
-28 + -2x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-14 + -1x + 3x2) = 0

Factor a trinomial.
2((-2 + -1x)(7 + -3x)) = 0

Ignore the factor 2.

Subproblem 1
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

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 = {-2, 2.333333333}

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