(5x+1)(-3x+4)+x(10x+2)=0

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Solution for (5x+1)(-3x+4)+x(10x+2)=0 equation: 


Simplifying
(5x + 1)(-3x + 4) + x(10x + 2) = 0

Reorder the terms:
(1 + 5x)(-3x + 4) + x(10x + 2) = 0

Reorder the terms:
(1 + 5x)(4 + -3x) + x(10x + 2) = 0

Multiply (1 + 5x) * (4 + -3x)
(1(4 + -3x) + 5x * (4 + -3x)) + x(10x + 2) = 0
((4 * 1 + -3x * 1) + 5x * (4 + -3x)) + x(10x + 2) = 0
((4 + -3x) + 5x * (4 + -3x)) + x(10x + 2) = 0
(4 + -3x + (4 * 5x + -3x * 5x)) + x(10x + 2) = 0
(4 + -3x + (20x + -15x2)) + x(10x + 2) = 0

Combine like terms: -3x + 20x = 17x
(4 + 17x + -15x2) + x(10x + 2) = 0

Reorder the terms:
4 + 17x + -15x2 + x(2 + 10x) = 0
4 + 17x + -15x2 + (2 * x + 10x * x) = 0
4 + 17x + -15x2 + (2x + 10x2) = 0

Reorder the terms:
4 + 17x + 2x + -15x2 + 10x2 = 0

Combine like terms: 17x + 2x = 19x
4 + 19x + -15x2 + 10x2 = 0

Combine like terms: -15x2 + 10x2 = -5x2
4 + 19x + -5x2 = 0

Solving
4 + 19x + -5x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(4 + -1x)(1 + 5x) = 0


Subproblem 1
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4

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

Simplifying
1 + 5x = 0

Solving
1 + 5x = 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 + 5x = 0 + -1

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

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

Divide each side by '5'.
x = -0.2

Simplifying
x = -0.2
Solution
x = {4, -0.2}

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