20x(x-5)+40=-55(2x-1)+15

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Solution for 20x(x-5)+40=-55(2x-1)+15 equation:


Simplifying
20x(x + -5) + 40 = -55(2x + -1) + 15

Reorder the terms:
20x(-5 + x) + 40 = -55(2x + -1) + 15
(-5 * 20x + x * 20x) + 40 = -55(2x + -1) + 15
(-100x + 20x2) + 40 = -55(2x + -1) + 15

Reorder the terms:
40 + -100x + 20x2 = -55(2x + -1) + 15

Reorder the terms:
40 + -100x + 20x2 = -55(-1 + 2x) + 15
40 + -100x + 20x2 = (-1 * -55 + 2x * -55) + 15
40 + -100x + 20x2 = (55 + -110x) + 15

Reorder the terms:
40 + -100x + 20x2 = 55 + 15 + -110x

Combine like terms: 55 + 15 = 70
40 + -100x + 20x2 = 70 + -110x

Solving
40 + -100x + 20x2 = 70 + -110x

Solving for variable 'x'.

Reorder the terms:
40 + -70 + -100x + 110x + 20x2 = 70 + -110x + -70 + 110x

Combine like terms: 40 + -70 = -30
-30 + -100x + 110x + 20x2 = 70 + -110x + -70 + 110x

Combine like terms: -100x + 110x = 10x
-30 + 10x + 20x2 = 70 + -110x + -70 + 110x

Reorder the terms:
-30 + 10x + 20x2 = 70 + -70 + -110x + 110x

Combine like terms: 70 + -70 = 0
-30 + 10x + 20x2 = 0 + -110x + 110x
-30 + 10x + 20x2 = -110x + 110x

Combine like terms: -110x + 110x = 0
-30 + 10x + 20x2 = 0

Factor out the Greatest Common Factor (GCF), '10'.
10(-3 + x + 2x2) = 0

Factor a trinomial.
10((-3 + -2x)(1 + -1x)) = 0

Ignore the factor 10.

Subproblem 1

Set the factor '(-3 + -2x)' equal to zero and attempt to solve: Simplifying -3 + -2x = 0 Solving -3 + -2x = 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 + -2x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -2x = 0 + 3 -2x = 0 + 3 Combine like terms: 0 + 3 = 3 -2x = 3 Divide each side by '-2'. x = -1.5 Simplifying x = -1.5

Subproblem 2

Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 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 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1

Solution

x = {-1.5, 1}

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