(2x-3)(5x+1)+(2x-3)(3x+4)=0

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Solution for (2x-3)(5x+1)+(2x-3)(3x+4)=0 equation: 


Simplifying
(2x + -3)(5x + 1) + (2x + -3)(3x + 4) = 0

Reorder the terms:
(-3 + 2x)(5x + 1) + (2x + -3)(3x + 4) = 0

Reorder the terms:
(-3 + 2x)(1 + 5x) + (2x + -3)(3x + 4) = 0

Multiply (-3 + 2x) * (1 + 5x)
(-3(1 + 5x) + 2x * (1 + 5x)) + (2x + -3)(3x + 4) = 0
((1 * -3 + 5x * -3) + 2x * (1 + 5x)) + (2x + -3)(3x + 4) = 0
((-3 + -15x) + 2x * (1 + 5x)) + (2x + -3)(3x + 4) = 0
(-3 + -15x + (1 * 2x + 5x * 2x)) + (2x + -3)(3x + 4) = 0
(-3 + -15x + (2x + 10x2)) + (2x + -3)(3x + 4) = 0

Combine like terms: -15x + 2x = -13x
(-3 + -13x + 10x2) + (2x + -3)(3x + 4) = 0

Reorder the terms:
-3 + -13x + 10x2 + (-3 + 2x)(3x + 4) = 0

Reorder the terms:
-3 + -13x + 10x2 + (-3 + 2x)(4 + 3x) = 0

Multiply (-3 + 2x) * (4 + 3x)
-3 + -13x + 10x2 + (-3(4 + 3x) + 2x * (4 + 3x)) = 0
-3 + -13x + 10x2 + ((4 * -3 + 3x * -3) + 2x * (4 + 3x)) = 0
-3 + -13x + 10x2 + ((-12 + -9x) + 2x * (4 + 3x)) = 0
-3 + -13x + 10x2 + (-12 + -9x + (4 * 2x + 3x * 2x)) = 0
-3 + -13x + 10x2 + (-12 + -9x + (8x + 6x2)) = 0

Combine like terms: -9x + 8x = -1x
-3 + -13x + 10x2 + (-12 + -1x + 6x2) = 0

Reorder the terms:
-3 + -12 + -13x + -1x + 10x2 + 6x2 = 0

Combine like terms: -3 + -12 = -15
-15 + -13x + -1x + 10x2 + 6x2 = 0

Combine like terms: -13x + -1x = -14x
-15 + -14x + 10x2 + 6x2 = 0

Combine like terms: 10x2 + 6x2 = 16x2
-15 + -14x + 16x2 = 0

Solving
-15 + -14x + 16x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-5 + -8x)(3 + -2x) = 0


Subproblem 1
Set the factor '(-5 + -8x)' equal to zero and attempt to solve:

Simplifying
-5 + -8x = 0

Solving
-5 + -8x = 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 + -8x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -8x = 0 + 5
-8x = 0 + 5

Combine like terms: 0 + 5 = 5
-8x = 5

Divide each side by '-8'.
x = -0.625

Simplifying
x = -0.625

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 = {-0.625, 1.5}

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