2(x+5)(x-2)-x(x+5)=52

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Solution for 2(x+5)(x-2)-x(x+5)=52 equation:


Simplifying
2(x + 5)(x + -2) + -1x(x + 5) = 52

Reorder the terms:
2(5 + x)(x + -2) + -1x(x + 5) = 52

Reorder the terms:
2(5 + x)(-2 + x) + -1x(x + 5) = 52

Multiply (5 + x) * (-2 + x)
2(5(-2 + x) + x(-2 + x)) + -1x(x + 5) = 52
2((-2 * 5 + x * 5) + x(-2 + x)) + -1x(x + 5) = 52
2((-10 + 5x) + x(-2 + x)) + -1x(x + 5) = 52
2(-10 + 5x + (-2 * x + x * x)) + -1x(x + 5) = 52
2(-10 + 5x + (-2x + x2)) + -1x(x + 5) = 52

Combine like terms: 5x + -2x = 3x
2(-10 + 3x + x2) + -1x(x + 5) = 52
(-10 * 2 + 3x * 2 + x2 * 2) + -1x(x + 5) = 52
(-20 + 6x + 2x2) + -1x(x + 5) = 52

Reorder the terms:
-20 + 6x + 2x2 + -1x(5 + x) = 52
-20 + 6x + 2x2 + (5 * -1x + x * -1x) = 52
-20 + 6x + 2x2 + (-5x + -1x2) = 52

Reorder the terms:
-20 + 6x + -5x + 2x2 + -1x2 = 52

Combine like terms: 6x + -5x = 1x
-20 + 1x + 2x2 + -1x2 = 52

Combine like terms: 2x2 + -1x2 = 1x2
-20 + 1x + 1x2 = 52

Solving
-20 + 1x + 1x2 = 52

Solving for variable 'x'.

Reorder the terms:
-20 + -52 + 1x + 1x2 = 52 + -52

Combine like terms: -20 + -52 = -72
-72 + 1x + 1x2 = 52 + -52

Combine like terms: 52 + -52 = 0
-72 + 1x + 1x2 = 0

Factor a trinomial.
(-9 + -1x)(8 + -1x) = 0

Subproblem 1

Set the factor '(-9 + -1x)' equal to zero and attempt to solve: Simplifying -9 + -1x = 0 Solving -9 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -1x = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1x = 0 + 9 -1x = 0 + 9 Combine like terms: 0 + 9 = 9 -1x = 9 Divide each side by '-1'. x = -9 Simplifying x = -9

Subproblem 2

Set the factor '(8 + -1x)' equal to zero and attempt to solve: Simplifying 8 + -1x = 0 Solving 8 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1x = 0 + -8 -1x = 0 + -8 Combine like terms: 0 + -8 = -8 -1x = -8 Divide each side by '-1'. x = 8 Simplifying x = 8

Solution

x = {-9, 8}

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