6x(-5x+5)=3x-21

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Solution for 6x(-5x+5)=3x-21 equation: 


Simplifying
6x(-5x + 5) = 3x + -21

Reorder the terms:
6x(5 + -5x) = 3x + -21
(5 * 6x + -5x * 6x) = 3x + -21
(30x + -30x2) = 3x + -21

Reorder the terms:
30x + -30x2 = -21 + 3x

Solving
30x + -30x2 = -21 + 3x

Solving for variable 'x'.

Reorder the terms:
21 + 30x + -3x + -30x2 = -21 + 3x + 21 + -3x

Combine like terms: 30x + -3x = 27x
21 + 27x + -30x2 = -21 + 3x + 21 + -3x

Reorder the terms:
21 + 27x + -30x2 = -21 + 21 + 3x + -3x

Combine like terms: -21 + 21 = 0
21 + 27x + -30x2 = 0 + 3x + -3x
21 + 27x + -30x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
21 + 27x + -30x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(7 + 9x + -10x2) = 0

Factor a trinomial.
3((7 + -5x)(1 + 2x)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(7 + -5x)' equal to zero and attempt to solve:

Simplifying
7 + -5x = 0

Solving
7 + -5x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -5x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -5x = 0 + -7
-5x = 0 + -7

Combine like terms: 0 + -7 = -7
-5x = -7

Divide each side by '-5'.
x = 1.4

Simplifying
x = 1.4

Subproblem 2
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
Solution
x = {1.4, -0.5}

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