4*5*(2*x+1)-7*5*(10*x+5)+2*(10*x+5)*(2*x+1)=0

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Solution for 4*5*(2*x+1)-7*5*(10*x+5)+2*(10*x+5)*(2*x+1)=0 equation: 


Simplifying
4 * 5(2x + 1) + -7 * 5(10x + 5) + 2(10x + 5)(2x + 1) = 0

Reorder the terms:
4 * 5(1 + 2x) + -7 * 5(10x + 5) + 2(10x + 5)(2x + 1) = 0

Multiply 4 * 5
20(1 + 2x) + -7 * 5(10x + 5) + 2(10x + 5)(2x + 1) = 0
(1 * 20 + 2x * 20) + -7 * 5(10x + 5) + 2(10x + 5)(2x + 1) = 0
(20 + 40x) + -7 * 5(10x + 5) + 2(10x + 5)(2x + 1) = 0

Reorder the terms:
20 + 40x + -7 * 5(5 + 10x) + 2(10x + 5)(2x + 1) = 0

Multiply -7 * 5
20 + 40x + -35(5 + 10x) + 2(10x + 5)(2x + 1) = 0
20 + 40x + (5 * -35 + 10x * -35) + 2(10x + 5)(2x + 1) = 0
20 + 40x + (-175 + -350x) + 2(10x + 5)(2x + 1) = 0

Reorder the terms:
20 + 40x + -175 + -350x + 2(5 + 10x)(2x + 1) = 0

Reorder the terms:
20 + 40x + -175 + -350x + 2(5 + 10x)(1 + 2x) = 0

Multiply (5 + 10x) * (1 + 2x)
20 + 40x + -175 + -350x + 2(5(1 + 2x) + 10x * (1 + 2x)) = 0
20 + 40x + -175 + -350x + 2((1 * 5 + 2x * 5) + 10x * (1 + 2x)) = 0
20 + 40x + -175 + -350x + 2((5 + 10x) + 10x * (1 + 2x)) = 0
20 + 40x + -175 + -350x + 2(5 + 10x + (1 * 10x + 2x * 10x)) = 0
20 + 40x + -175 + -350x + 2(5 + 10x + (10x + 20x2)) = 0

Combine like terms: 10x + 10x = 20x
20 + 40x + -175 + -350x + 2(5 + 20x + 20x2) = 0
20 + 40x + -175 + -350x + (5 * 2 + 20x * 2 + 20x2 * 2) = 0
20 + 40x + -175 + -350x + (10 + 40x + 40x2) = 0

Reorder the terms:
20 + -175 + 10 + 40x + -350x + 40x + 40x2 = 0

Combine like terms: 20 + -175 = -155
-155 + 10 + 40x + -350x + 40x + 40x2 = 0

Combine like terms: -155 + 10 = -145
-145 + 40x + -350x + 40x + 40x2 = 0

Combine like terms: 40x + -350x = -310x
-145 + -310x + 40x + 40x2 = 0

Combine like terms: -310x + 40x = -270x
-145 + -270x + 40x2 = 0

Solving
-145 + -270x + 40x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-29 + -54x + 8x2) = 0

Factor a trinomial.
5((-1 + -2x)(29 + -4x)) = 0

Ignore the factor 5.

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

Simplifying
-1 + -2x = 0

Solving
-1 + -2x = 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 + -2x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2x = 0 + 1
-2x = 0 + 1

Combine like terms: 0 + 1 = 1
-2x = 1

Divide each side by '-2'.
x = -0.5

Simplifying
x = -0.5

Subproblem 2
Set the factor '(29 + -4x)' equal to zero and attempt to solve:

Simplifying
29 + -4x = 0

Solving
29 + -4x = 0

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

Add '-29' to each side of the equation.
29 + -29 + -4x = 0 + -29

Combine like terms: 29 + -29 = 0
0 + -4x = 0 + -29
-4x = 0 + -29

Combine like terms: 0 + -29 = -29
-4x = -29

Divide each side by '-4'.
x = 7.25

Simplifying
x = 7.25
Solution
x = {-0.5, 7.25}

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