(x-3)(x-3)-(2x+5)(2x+5)=-16

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Solution for (x-3)(x-3)-(2x+5)(2x+5)=-16 equation:


Simplifying
(x + -3)(x + -3) + -1(2x + 5)(2x + 5) = -16

Reorder the terms:
(-3 + x)(x + -3) + -1(2x + 5)(2x + 5) = -16

Reorder the terms:
(-3 + x)(-3 + x) + -1(2x + 5)(2x + 5) = -16

Multiply (-3 + x) * (-3 + x)
(-3(-3 + x) + x(-3 + x)) + -1(2x + 5)(2x + 5) = -16
((-3 * -3 + x * -3) + x(-3 + x)) + -1(2x + 5)(2x + 5) = -16
((9 + -3x) + x(-3 + x)) + -1(2x + 5)(2x + 5) = -16
(9 + -3x + (-3 * x + x * x)) + -1(2x + 5)(2x + 5) = -16
(9 + -3x + (-3x + x2)) + -1(2x + 5)(2x + 5) = -16

Combine like terms: -3x + -3x = -6x
(9 + -6x + x2) + -1(2x + 5)(2x + 5) = -16

Reorder the terms:
9 + -6x + x2 + -1(5 + 2x)(2x + 5) = -16

Reorder the terms:
9 + -6x + x2 + -1(5 + 2x)(5 + 2x) = -16

Multiply (5 + 2x) * (5 + 2x)
9 + -6x + x2 + -1(5(5 + 2x) + 2x * (5 + 2x)) = -16
9 + -6x + x2 + -1((5 * 5 + 2x * 5) + 2x * (5 + 2x)) = -16
9 + -6x + x2 + -1((25 + 10x) + 2x * (5 + 2x)) = -16
9 + -6x + x2 + -1(25 + 10x + (5 * 2x + 2x * 2x)) = -16
9 + -6x + x2 + -1(25 + 10x + (10x + 4x2)) = -16

Combine like terms: 10x + 10x = 20x
9 + -6x + x2 + -1(25 + 20x + 4x2) = -16
9 + -6x + x2 + (25 * -1 + 20x * -1 + 4x2 * -1) = -16
9 + -6x + x2 + (-25 + -20x + -4x2) = -16

Reorder the terms:
9 + -25 + -6x + -20x + x2 + -4x2 = -16

Combine like terms: 9 + -25 = -16
-16 + -6x + -20x + x2 + -4x2 = -16

Combine like terms: -6x + -20x = -26x
-16 + -26x + x2 + -4x2 = -16

Combine like terms: x2 + -4x2 = -3x2
-16 + -26x + -3x2 = -16

Add '16' to each side of the equation.
-16 + -26x + 16 + -3x2 = -16 + 16

Reorder the terms:
-16 + 16 + -26x + -3x2 = -16 + 16

Combine like terms: -16 + 16 = 0
0 + -26x + -3x2 = -16 + 16
-26x + -3x2 = -16 + 16

Combine like terms: -16 + 16 = 0
-26x + -3x2 = 0

Solving
-26x + -3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-1x'.
-1x(26 + 3x) = 0

Ignore the factor -1.

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 '(26 + 3x)' equal to zero and attempt to solve: Simplifying 26 + 3x = 0 Solving 26 + 3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-26' to each side of the equation. 26 + -26 + 3x = 0 + -26 Combine like terms: 26 + -26 = 0 0 + 3x = 0 + -26 3x = 0 + -26 Combine like terms: 0 + -26 = -26 3x = -26 Divide each side by '3'. x = -8.666666667 Simplifying x = -8.666666667

Solution

x = {0, -8.666666667}

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