(2x-5)(4x+3)+7x=0

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Solution for (2x-5)(4x+3)+7x=0 equation: 


Simplifying
(2x + -5)(4x + 3) + 7x = 0

Reorder the terms:
(-5 + 2x)(4x + 3) + 7x = 0

Reorder the terms:
(-5 + 2x)(3 + 4x) + 7x = 0

Multiply (-5 + 2x) * (3 + 4x)
(-5(3 + 4x) + 2x * (3 + 4x)) + 7x = 0
((3 * -5 + 4x * -5) + 2x * (3 + 4x)) + 7x = 0
((-15 + -20x) + 2x * (3 + 4x)) + 7x = 0
(-15 + -20x + (3 * 2x + 4x * 2x)) + 7x = 0
(-15 + -20x + (6x + 8x2)) + 7x = 0

Combine like terms: -20x + 6x = -14x
(-15 + -14x + 8x2) + 7x = 0

Reorder the terms:
-15 + -14x + 7x + 8x2 = 0

Combine like terms: -14x + 7x = -7x
-15 + -7x + 8x2 = 0

Solving
-15 + -7x + 8x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-1 + -1x)(15 + -8x) = 0


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

Simplifying
-1 + -1x = 0

Solving
-1 + -1x = 0

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

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

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

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

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

Simplifying
x = -1

Subproblem 2
Set the factor '(15 + -8x)' equal to zero and attempt to solve:

Simplifying
15 + -8x = 0

Solving
15 + -8x = 0

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

Add '-15' to each side of the equation.
15 + -15 + -8x = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -8x = 0 + -15
-8x = 0 + -15

Combine like terms: 0 + -15 = -15
-8x = -15

Divide each side by '-8'.
x = 1.875

Simplifying
x = 1.875
Solution
x = {-1, 1.875}

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