-2x(5x-3)+9=-10x+15

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Solution for -2x(5x-3)+9=-10x+15 equation: 


Simplifying
-2x(5x + -3) + 9 = -10x + 15

Reorder the terms:
-2x(-3 + 5x) + 9 = -10x + 15
(-3 * -2x + 5x * -2x) + 9 = -10x + 15
(6x + -10x2) + 9 = -10x + 15

Reorder the terms:
9 + 6x + -10x2 = -10x + 15

Reorder the terms:
9 + 6x + -10x2 = 15 + -10x

Solving
9 + 6x + -10x2 = 15 + -10x

Solving for variable 'x'.

Reorder the terms:
9 + -15 + 6x + 10x + -10x2 = 15 + -10x + -15 + 10x

Combine like terms: 9 + -15 = -6
-6 + 6x + 10x + -10x2 = 15 + -10x + -15 + 10x

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

Reorder the terms:
-6 + 16x + -10x2 = 15 + -15 + -10x + 10x

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

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

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + 8x + -5x2) = 0

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

Ignore the factor 2.

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

Simplifying
-1 + x = 0

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

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

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

Simplifying
x = 1

Subproblem 2
Set the factor '(3 + -5x)' equal to zero and attempt to solve:

Simplifying
3 + -5x = 0

Solving
3 + -5x = 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 + -5x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -5x = 0 + -3
-5x = 0 + -3

Combine like terms: 0 + -3 = -3
-5x = -3

Divide each side by '-5'.
x = 0.6

Simplifying
x = 0.6
Solution
x = {1, 0.6}

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