6(5x-1)(5x-1)+4=-14(5x-1)

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Solution for 6(5x-1)(5x-1)+4=-14(5x-1) equation:


Simplifying
6(5x + -1)(5x + -1) + 4 = -14(5x + -1)

Reorder the terms:
6(-1 + 5x)(5x + -1) + 4 = -14(5x + -1)

Reorder the terms:
6(-1 + 5x)(-1 + 5x) + 4 = -14(5x + -1)

Multiply (-1 + 5x) * (-1 + 5x)
6(-1(-1 + 5x) + 5x * (-1 + 5x)) + 4 = -14(5x + -1)
6((-1 * -1 + 5x * -1) + 5x * (-1 + 5x)) + 4 = -14(5x + -1)
6((1 + -5x) + 5x * (-1 + 5x)) + 4 = -14(5x + -1)
6(1 + -5x + (-1 * 5x + 5x * 5x)) + 4 = -14(5x + -1)
6(1 + -5x + (-5x + 25x2)) + 4 = -14(5x + -1)

Combine like terms: -5x + -5x = -10x
6(1 + -10x + 25x2) + 4 = -14(5x + -1)
(1 * 6 + -10x * 6 + 25x2 * 6) + 4 = -14(5x + -1)
(6 + -60x + 150x2) + 4 = -14(5x + -1)

Reorder the terms:
6 + 4 + -60x + 150x2 = -14(5x + -1)

Combine like terms: 6 + 4 = 10
10 + -60x + 150x2 = -14(5x + -1)

Reorder the terms:
10 + -60x + 150x2 = -14(-1 + 5x)
10 + -60x + 150x2 = (-1 * -14 + 5x * -14)
10 + -60x + 150x2 = (14 + -70x)

Solving
10 + -60x + 150x2 = 14 + -70x

Solving for variable 'x'.

Reorder the terms:
10 + -14 + -60x + 70x + 150x2 = 14 + -70x + -14 + 70x

Combine like terms: 10 + -14 = -4
-4 + -60x + 70x + 150x2 = 14 + -70x + -14 + 70x

Combine like terms: -60x + 70x = 10x
-4 + 10x + 150x2 = 14 + -70x + -14 + 70x

Reorder the terms:
-4 + 10x + 150x2 = 14 + -14 + -70x + 70x

Combine like terms: 14 + -14 = 0
-4 + 10x + 150x2 = 0 + -70x + 70x
-4 + 10x + 150x2 = -70x + 70x

Combine like terms: -70x + 70x = 0
-4 + 10x + 150x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-2 + 5x + 75x2) = 0

Factor a trinomial.
2((-1 + -5x)(2 + -15x)) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-1 + -5x)' equal to zero and attempt to solve: Simplifying -1 + -5x = 0 Solving -1 + -5x = 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 + -5x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -5x = 0 + 1 -5x = 0 + 1 Combine like terms: 0 + 1 = 1 -5x = 1 Divide each side by '-5'. x = -0.2 Simplifying x = -0.2

Subproblem 2

Set the factor '(2 + -15x)' equal to zero and attempt to solve: Simplifying 2 + -15x = 0 Solving 2 + -15x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -15x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -15x = 0 + -2 -15x = 0 + -2 Combine like terms: 0 + -2 = -2 -15x = -2 Divide each side by '-15'. x = 0.1333333333 Simplifying x = 0.1333333333

Solution

x = {-0.2, 0.1333333333}

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