2x(3x+5)+x(6x-7)=

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Solution for 2x(3x+5)+x(6x-7)= equation: 


Simplifying
2x(3x + 5) + x(6x + -7) = 0

Reorder the terms:
2x(5 + 3x) + x(6x + -7) = 0
(5 * 2x + 3x * 2x) + x(6x + -7) = 0
(10x + 6x2) + x(6x + -7) = 0

Reorder the terms:
10x + 6x2 + x(-7 + 6x) = 0
10x + 6x2 + (-7 * x + 6x * x) = 0
10x + 6x2 + (-7x + 6x2) = 0

Reorder the terms:
10x + -7x + 6x2 + 6x2 = 0

Combine like terms: 10x + -7x = 3x
3x + 6x2 + 6x2 = 0

Combine like terms: 6x2 + 6x2 = 12x2
3x + 12x2 = 0

Solving
3x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x'.
3x(1 + 4x) = 0

Ignore the factor 3.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(1 + 4x)' equal to zero and attempt to solve:

Simplifying
1 + 4x = 0

Solving
1 + 4x = 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 + 4x = 0 + -1

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

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

Divide each side by '4'.
x = -0.25

Simplifying
x = -0.25
Solution
x = {0, -0.25}

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